Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81801	Find the Derivative - d/dt	(2t^(9/2))/3	$\frac{2 t^{\frac{9}{2}}}{3}$
81802	Find dy/dx	-y^2+x^2=-2+xy	$- y^{2} + x^{2} = - 2 + x y$
81803	Find the Derivative of the Integral	F(x) = integral from 3 to x of (tan(5t)sec(5t)-1) with respect to t	$F (x) = \int_{3}^{x} (\tan (5 t) \sec (5 t) - 1) d t$
81804	Find the Concavity	f(x)=1/5x^5+x^4	$f (x) = \frac{1}{5} x^{5} + x^{4}$
81805	Find the Derivative - d/dx	(3/(x^2+z^2))	$(\frac{3}{(x^{2} + z^{2})})$
81806	Find Where Increasing/Decreasing	f(x)=(x^2-3)e^(-x)	$f (x) = (x^{2} - 3) e^{- x}$
81807	Find dy/dx	y=sec(x)+tan(x)	$y = \sec (x) + \tan (x)$
81808	Find dy/dx	y=5x(x^2+6)	$y = 5 x (x^{2} + 6)$
81809	Evaluate Using Summation Formulas	sum from 0 to 10 of x^2-2x+9	$\sum_{0}^{10} x^{2} - 2 x + 9$
81810	Find dy/dx	y=(2x)/(x+1)	$y = \frac{2 x}{x + 1}$
81811	Evaluate the Limit	limit as x approaches 1 of 2/(x^2-1)-1/(x-1)	$lim_{x \to 1} \frac{2}{x^{2} - 1} - \frac{1}{x - 1}$
81812	Find dy/dx	y=4x^3-7x^2+3x-2	$y = 4 x^{3} - 7 x^{2} + 3 x - 2$
81813	Find the Derivative - d/dx	square root of 3cos(x)^3	$\sqrt{3 \cos^{3} (x)}$
81814	Find the Antiderivative	tan(x)sec(x)	$\tan (x) \sec (x)$
81815	Find dy/dx	2-4y^2+3x^3=3y-5y^3	$2 - 4 y^{2} + 3 x^{3} = 3 y - 5 y^{3}$
81816	Evaluate the Limit	limit as x approaches 3 of (x^4-3x^3)/(9-x^2)	$lim_{x \to 3} \frac{x^{4} - 3 x^{3}}{9 - x^{2}}$
81817	Find the Antiderivative	x^3e^(x^2)	$x^{3} e^{x^{2}}$
81818	Find the Antiderivative	2csc(x/3)^2	$2 \csc^{2} (\frac{x}{3})$
81819	Evaluate the Integral	integral from 0 to pi/2 of cos(x)^11sin(x)^5 with respect to x	$\int_{0}^{\frac{π}{2}} \cos^{11} (x) \sin^{5} (x) d x$
81820	Find the Slope	f(x)=x-5	$f (x) = x - 5$
81821	Evaluate the Integral	integral from 0 to 2 of (x^2-1)e^(x^3-3x+1) with respect to x	$\int_{0}^{2} (x^{2} - 1) e^{x^{3} - 3 x + 1} d x$
81822	Find dy/dx	-xy^2-3+2x^3=-3y^3	$- x y^{2} - 3 + 2 x^{3} = - 3 y^{3}$
81823	Evaluate the Limit	limit as x approaches pi/(()/())*2 of xcos(x)	$lim_{x \to \frac{π}{\frac{}{}} \cdot 2} x \cos (x)$
81824	Evaluate the Limit	limit as x approaches 1 of -(7x^2-5x-4)(x^(1/3)+8)	$lim_{x \to 1} - (7 x^{2} - 5 x - 4) (x^{\frac{1}{3}} + 8)$
81825	Find the Second Derivative	y=e^(-x)+2xe^(-x)+x^2e^(-x)	$y = e^{- x} + 2 x e^{- x} + x^{2} e^{- x}$
81826	Find the Maximum/Minimum Value	f(x)=-\|x+1\|+6	$f (x) = - \| x + 1 \| + 6$
81827	Find dy/dx	-4+x=x^2y+4y^2	$- 4 + x = x^{2} y + 4 y^{2}$
81828	Find the Derivative - d/dx	2x^2(3x-4)	$2 x^{2} (3 x - 4)$
81829	Find Where Increasing/Decreasing	g(x)=1/3x^3+3/2x^2-70x+5	$g (x) = \frac{1}{3} x^{3} + \frac{3}{2} x^{2} - 70 x + 5$
81830	Evaluate the Integral	integral from 6 to infinity of 5/((x-1)( natural log of x-1)^3) with respect to x	$\int_{6}^{\infty} \frac{5}{(x - 1) \ln^{3} (x - 1)} d x$
81831	Evaluate the Limit	limit as x approaches infinity of (1+(3(a^2+1))/(5x^2))^x	$lim_{x \to \infty} {(1 + \frac{3 (a^{2} + 1)}{5 x^{2}})}^{x}$
81832	Evaluate the Limit	limit as x approaches infinity of (4x^3-2x^2+5x-7)/(x^2-4x-2x^3-1)	$lim_{x \to \infty} \frac{4 x^{3} - 2 x^{2} + 5 x - 7}{x^{2} - 4 x - 2 x^{3} - 1}$
81833	Evaluate the Integral	integral of y^2(4-y^3)^(2/3) with respect to y	$\int y^{2} {(4 - y^{3})}^{\frac{2}{3}} d y$
81834	Evaluate the Integral	integral from 0 to 2 of x square root of 1+2x^2 with respect to x	$\int_{0}^{2} x \sqrt{1 + 2 x^{2}} d x$
81835	Find the Antiderivative	f(x)=1/(x^2)-2sin(x)	$f (x) = \frac{1}{x^{2}} - 2 \sin (x)$
81836	Evaluate the Integral	integral of 4x(5x^2) with respect to x	$\int 4 x (5 x^{2}) d x$
81837	Find the Antiderivative	f(x)=1/((x+1)^2)	$f (x) = \frac{1}{{(x + 1)}^{2}}$
81838	Find dy/dx	-y^2-2x^3=y	$- y^{2} - 2 x^{3} = y$
81839	Find the Maximum/Minimum Value	f(x)=3sin(x/2)+4	$f (x) = 3 \sin (\frac{x}{2}) + 4$
81840	Find the Derivative - d/dw	wtf	$w t f$
81841	Evaluate the Limit	limit as x approaches infinity of (x root of 3)/9	$lim_{x \to \infty} \frac{\sqrt[x]{3}}{9}$
81842	Evaluate the Limit	limit as y approaches 2 of ((4y^3+8y)/(y+4))^(1/3)	$lim_{y \to 2} {(\frac{4 y^{3} + 8 y}{y + 4})}^{\frac{1}{3}}$
81843	Evaluate the Integral	integral from 1 to infinity of e^x with respect to x	$\int_{1}^{\infty} e^{x} d x$
81844	Find the Maximum/Minimum Value	f(x)=-1/2x^4+8x^3-32x^2-5	$f (x) = - \frac{1}{2} x^{4} + 8 x^{3} - 32 x^{2} - 5$
81845	Find the Derivative - d/dx	(4-1/3x^2)^3	${(4 - \frac{1}{3} x^{2})}^{3}$
81846	Evaluate the Limit	limit as x approaches infinity of 250-e^(-x)	$lim_{x \to \infty} 250 - e^{- x}$
81847	Find the Derivative - d/dx	( square root of x+1-1)/x	$\frac{\sqrt{x + 1} - 1}{x}$
81848	Find the Derivative - d/dx	natural log of 2-e^x	$\ln (2 - e^{x})$
81849	Evaluate the Limit	limit as x approaches -3 of (x^2-9)/( square root of x+7-2)	$lim_{x \to - 3} \frac{x^{2} - 9}{\sqrt{x + 7} - 2}$
81850	Find the Maximum/Minimum Value	f(x)=x^3-3/2x^2-36x	$f (x) = x^{3} - \frac{3}{2} x^{2} - 36 x$
81851	Find the Derivative Using Chain Rule - d/dx	y=(sin(x^3+7)^5)^9	$y = {(\sin^{5} (x^{3} + 7))}^{9}$
81852	Evaluate the Integral	integral from 0 to pi/2 of cos(x)^9sin(x)^5 with respect to x	$\int_{0}^{\frac{π}{2}} \cos^{9} (x) \sin^{5} (x) d x$
81853	Evaluate the Integral	integral from 0 to pi/3 of square root of 1+tan(x)^2 with respect to x	$\int_{0}^{\frac{π}{3}} \sqrt{1 + \tan^{2} (x)} d x$
81854	Find the Turning Points	f(x)=-x^3-11x^2-28x	$f (x) = - x^{3} - 11 x^{2} - 28 x$
81855	Evaluate the Integral	integral from 1 to infinity of 1/( square root of pix) with respect to x	$\int_{1}^{\infty} \frac{1}{\sqrt{π x}} d x$
81856	Find the Antiderivative	1/e	$\frac{1}{e}$
81857	Find the Derivative - d/dy	1+2xe^y	$1 + 2 x e^{y}$
81858	Evaluate the Limit	limit as x approaches 1/4 of 2x^2-7	$lim_{x \to \frac{1}{4}} 2 x^{2} - 7$
81859	Integrate Using u-Substitution	integral from 0 to pi/4 of (sin(t))/(cos(t)^2) with respect to t	$\int_{0}^{\frac{π}{4}} \frac{\sin (t)}{\cos^{2} (t)} d t$
81860	Find dy/dx	1+3y^3-5y^2+x^2=0	$1 + 3 y^{3} - 5 y^{2} + x^{2} = 0$
81861	Evaluate the Integral	integral of (6 square root of x^3+7 cube root of x^2) with respect to x	$\int (6 \sqrt{x^{3}} + 7 \sqrt[3]{x^{2}}) d x$
81862	Find the Absolute Max and Min over the Interval	f(x)=x^3-3x^2+12	$f (x) = x^{3} - 3 x^{2} + 12$
81863	Evaluate the Integral	integral of (sin(x))/( square root of 4+cos(x)^2) with respect to x	$\int \frac{\sin (x)}{\sqrt{4 + \cos^{2} (x)}} d x$
81864	Find the Antiderivative	3cos(x)-x	$3 \cos (x) - x$
81865	Evaluate the Integral	integral from -2 to 2 of (x^7+k) with respect to x=16	$\int_{- 2}^{2} (x^{7} + k) d x = 16$
81866	Find the Antiderivative	f(x)=x square root of x	$f (x) = x \sqrt{x}$
81867	Determine if Continuous	f(x)=(x^2-9)/(x+3) if x!=-3; -6 if x=-3	$f (x) = {\begin{cases} \frac{x^{2} - 9}{x + 3} & x \neq - 3 \\ - 6 & x = - 3 \end{cases}$
81868	Evaluate the Integral	integral from 1/12 to 1/4 of csc(2pit)cot(2pit) with respect to t	$\int_{\frac{1}{12}}^{\frac{1}{4}} \csc (2 π t) \cot (2 π t) d t$
81869	Find the Derivative of the Integral	integral of (x-1)(x+a) with respect to x	$\int (x - 1) (x + a) d x$
81870	Find the Derivative - d/dx	y=(x-6)/(4x)	$y = \frac{x - 6}{4 x}$
81871	Evaluate the Integral	integral from 1 to 3 of (x-2)/(x^2-4x) with respect to x	$\int_{1}^{3} \frac{x - 2}{x^{2} - 4 x} d x$
81872	Find the Derivative - d/dx	J (x)=(3/2x^2-2)^2	$J$ $(x) = {(\frac{3}{2} x^{2} - 2)}^{2}$
81873	Integrate Using u-Substitution	integral of (1+x)/(1+x^2) with respect to x	$\int \frac{1 + x}{1 + x^{2}} d x$
81874	Integrate Using u-Substitution	integral of sec(x) with respect to x	$\int \sec (x) d x$
81875	Find the Slope at (1/2,32) Using Implicit Differentiation	f(t)=t^-5 ;, (1/2,32)	$f (t) = t^{- 5}$ ;, $(\frac{1}{2}, 32)$
81876	Evaluate the Limit	limit as x approaches 1 of 4x-1=3	$lim_{x \to 1} 4 x - 1 = 3$
81877	Find the Antiderivative	(x^2)/( square root of 1-x^2)	$\frac{x^{2}}{\sqrt{1 - x^{2}}}$
81878	Find dy/dx	-y^3-3=3y^2+4x^3	$- y^{3} - 3 = 3 y^{2} + 4 x^{3}$
81879	Find the Derivative - d/dx	1+1/(x^2)	$1 + \frac{1}{x^{2}}$
81880	Evaluate the Limit	limit as x approaches 4 of (x^2-6x+8)/(2x^3-4x^2-16x)	$lim_{x \to 4} \frac{x^{2} - 6 x + 8}{2 x^{3} - 4 x^{2} - 16 x}$
81881	Evaluate the Integral	integral from 0 to 3 of 1/((1-x)^2) with respect to x	$\int_{0}^{3} \frac{1}{{(1 - x)}^{2}} d x$
81882	Evaluate the Integral	integral of 3x^3(x^5+4/(x^4)) with respect to x	$\int 3 x^{3} (x^{5} + \frac{4}{x^{4}}) d x$
81883	Find the Derivative - d/dx	2cos(x)+1	$2 \cos (x) + 1$
81884	Evaluate the Integral	integral from 3 to 5 of (3x+5)/(x^2+2x-3) with respect to x	$\int_{3}^{5} \frac{3 x + 5}{x^{2} + 2 x - 3} d x$
81885	Evaluate the Limit	limit as x approaches 0 of (sin(x)-sinh(x))/(cos(x)-cosh(x))	$lim_{x \to 0} \frac{\sin (x) - \sinh (x)}{\cos (x) - \cosh (x)}$
81886	Find the Tangent Line at (2,-5)	16x^3+y^3=3 , (2,-5)	$16 x^{3} + y^{3} = 3$ , $(2, - 5)$
81887	Solve the Differential Equation	y'=2xy	$y' = 2 x y$
81888	Find the Antiderivative	xsin(x)^2	$x \sin^{2} (x)$
81889	Integrate Using u-Substitution	integral of 1/(2x) with respect to x	$\int \frac{1}{2 x} d x$
81890	Find the Maximum/Minimum Value	f(x)=4-45x+3x^2+x^3	$f (x) = 4 - 45 x + 3 x^{2} + x^{3}$
81891	Evaluate the Integral	integral of 2x^2(x-2)(4x-5) with respect to x	$\int 2 x^{2} (x - 2) (4 x - 5) d x$
81892	Find the Derivative - d/dx	-1/x+1	$- \frac{1}{x} + 1$
81893	Find the Antiderivative	natural log of x+2	$\ln (x + 2)$
81894	Find the Derivative - d/dx	(1- square root of x)(1- cube root of x)	$(1 - \sqrt{x}) (1 - \sqrt[3]{x})$
81895	Find the Maximum/Minimum Value	f(x)=2 square root of x+1-2	$f (x) = 2 \sqrt{x + 1} - 2$
81896	Evaluate the Integral	integral of x^2(2x-1)(x-6) with respect to x	$\int x^{2} (2 x - 1) (x - 6) d x$
81897	Find dy/dx	-x^3+4y^2=2y^3	$- x^{3} + 4 y^{2} = 2 y^{3}$
81898	Evaluate the Limit	limit as x approaches 0 of (5x^3+8x^3)/(3x^4-16x^2)	$lim_{x \to 0} \frac{5 x^{3} + 8 x^{3}}{3 x^{4} - 16 x^{2}}$
81899	Find dy/dx	y^2+x^2=-xy+3	$y^{2} + x^{2} = - x y + 3$
81900	Evaluate the Integral	integral from 0 to 3 of 6/(9+x^2) with respect to x	$\int_{0}^{3} \frac{6}{9 + x^{2}} d x$