Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83801	Find Where Increasing/Decreasing	f(x)=-e^x	$f (x) = - e^{x}$
83802	Evaluate the Integral	integral of (ax^2+bx+c) with respect to x	$\int (a x^{2} + b x + c) d x$
83803	Find the Third Derivative	f(x)=-1/3x^4+2x^2+x	$f (x) = - \frac{1}{3} x^{4} + 2 x^{2} + x$
83804	Find Where Increasing/Decreasing	f(x)=2e^x	$f (x) = 2 e^{x}$
83805	Find the Derivative - d/dx	natural log of xx-x	$\ln (x) x - x$
83806	Find the Derivative - d/dy	300 cube root of x^2 fourth root of y-100x-150y+2021	$300 \sqrt[3]{x^{2}} \sqrt[4]{y} - 100 x - 150 y + 2021$
83807	Find the Derivative - d/dx	-1/(3x^2)	$- \frac{1}{3 x^{2}}$
83808	Find the Maximum/Minimum Value	f(x)=1/3x^3+1/2x^2-6x	$f (x) = \frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x$
83809	Evaluate the Integral	integral of x^2arcsin(x) with respect to x	$\int x^{2} \arcsin (x) d x$
83810	Find the Antiderivative	f(x)=1/x-2e^x	$f (x) = \frac{1}{x} - 2 e^{x}$
83811	Evaluate the Integral	integral from negative infinity to 0 of 1/( fourth root of 5e^x) with respect to x	$\int_{- \infty}^{0} \frac{1}{\sqrt[4]{5 e^{x}}} d x$
83812	Find dy/dx	x^4+sin(y)=x^3y^2	$x^{4} + \sin (y) = x^{3} y^{2}$
83813	Find the Local Maxima and Minima	f(x)=10/3x^3-x^2-8x+48	$f (x) = \frac{10}{3} x^{3} - x^{2} - 8 x + 48$
83814	Evaluate the Integral	integral of (-e^(1/x))/(x^2) with respect to x	$\int \frac{- e^{\frac{1}{x}}}{x^{2}} d x$
83815	Find Where Increasing/Decreasing	f(x)=x^(1/3)+1	$f (x) = x^{\frac{1}{3}} + 1$
83816	Evaluate the Limit	limit as x approaches 0 of cube root of 3/(2x-1)	$lim_{x \to 0} \sqrt[3]{\frac{3}{2 x - 1}}$
83817	Find Where Increasing/Decreasing	f(x)=4*(3/8)^x	$f (x) = 4 \cdot {(\frac{3}{8})}^{x}$
83818	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (4 natural log of 1-2x+2x^3)/(5x^2+4x)	$lim_{x \to 0} \frac{4 \ln (1 - 2 x) + 2 x^{3}}{5 x^{2} + 4 x}$
83819	Find the Derivative - d/dx	cos(x/2)^2	$\cos^{2} (\frac{x}{2})$
83820	Evaluate the Integral	integral of (16x^4-3x^3+8x)/(x^3) with respect to x	$\int \frac{16 x^{4} - 3 x^{3} + 8 x}{x^{3}} d x$
83821	Find dy/dx	y = natural log of (5x-4)/(x seventh root of x^2+1)	$y = \ln (\frac{5 x - 4}{x \sqrt[7]{x^{2} + 1}})$
83822	Find the Derivative - d/dx	y=x^2(2x^3-1)^3	$y = x^{2} {(2 x^{3} - 1)}^{3}$
83823	Evaluate the Integral	integral of (sec(2x)+tan(2x)) with respect to x	$\int (\sec (2 x) + \tan (2 x)) d x$
83824	Find dy/dx	y=5x square root of x^2+1	$y = 5 x \sqrt{x^{2} + 1}$
83825	Find the Antiderivative	f(x)=3cos(x)-4sin(x)	$f (x) = 3 \cos (x) - 4 \sin (x)$
83826	Find the Derivative of the Integral	g(x) = integral from 0 to x of (t^2-t)/( square root of t) with respect to t	$g (x) = \int_{0}^{x} \frac{t^{2} - t}{\sqrt{t}} d t$
83827	Evaluate the Integral	Evaluate integral of -24x^5 with respect to x	Evaluate $\int - 24 x^{5} d x$
83828	Find the Antiderivative	f(x)=1/(2 square root of x)+1	$f (x) = \frac{1}{2 \sqrt{x}} + 1$
83829	Evaluate the Summation	sum from k=1 to 4 of (-1)^(k+1)k	$\sum_{k = 1}^{4} {(- 1)}^{k + 1} k$
83830	Find dy/dx	y=3/(sin(x)+cos(x))	$y = \frac{3}{\sin (x) + \cos (x)}$
83831	Find the Antiderivative	4-2/(x^3)	$4 - \frac{2}{x^{3}}$
83832	Find the Derivative - d/dx	1/(\|x\|)	$\frac{1}{\| x \|}$
83833	Find dy/dx	y=(x+1)/x	$y = \frac{x + 1}{x}$
83834	Find dy/dx	y=e^(8x+9)	$y = e^{8 x + 9}$
83835	Evaluate the Integral	integral from 0 to pi/4 of cos(2x)e^(sin(2x)) with respect to x	$\int_{0}^{\frac{π}{4}} \cos (2 x) e^{\sin (2 x)} d x$
83836	Find the Derivative - d/dx	(2x)/( square root of 5-3x^2)	$\frac{2 x}{\sqrt{5 - 3 x^{2}}}$
83837	Determine if Continuous	f(x)=(x^2+6x+9)/(x+3) if x!=-3; 9 if x=-3	$f (x) = {\begin{cases} \frac{x^{2} + 6 x + 9}{x + 3} & x \neq - 3 \\ 9 & x = - 3 \end{cases}$
83838	Integrate Using u-Substitution	integral of 1/( square root of 9-x^2) with respect to x	$\int \frac{1}{\sqrt{9 - x^{2}}} d x$
83839	Evaluate the Integral	integral of 5/((1-x)^2) with respect to x	$\int \frac{5}{{(1 - x)}^{2}} d x$
83840	Find dx/dy	y=sec(x)+tan(x)	$y = \sec (x) + \tan (x)$
83841	Evaluate the Limit	limit as x approaches pi/4 of tan((4x)/3)	$lim_{x \to \frac{π}{4}} \tan (\frac{4 x}{3})$
83842	Evaluate the Limit	limit as x approaches 0 of ((3x-1)^5+1)/(5x)	$lim_{x \to 0} \frac{{(3 x - 1)}^{5} + 1}{5 x}$
83843	Find the Derivative - d/dx	(d((x^2cos(x))/(sin(x))))/(dx)	$\frac{d (\frac{x^{2} \cos (x)}{\sin (x)})}{d x}$
83844	Integrate Using u-Substitution	integral of sec(2x)tan(2x) with respect to x	$\int \sec (2 x) \tan (2 x) d x$
83845	Evaluate the Integral	Evaluate integral of (-4x^-3-20x^-5) with respect to x	Evaluate $\int (- 4 x^{- 3} - 20 x^{- 5}) d x$
83846	Find the Derivative - d/dx	(x-2)^3(x+1)^4	${(x - 2)}^{3} {(x + 1)}^{4}$
83847	Find the Antiderivative	f(x)=e^(2x-1)	$f (x) = e^{2 x - 1}$
83848	Find the Derivative - d/dx	sin(-3x^2-3x+7)	$\sin (- 3 x^{2} - 3 x + 7)$
83849	Find the Maximum/Minimum Value	y=x^3-x	$y = x^{3} - x$
83850	Find the Derivative of the Integral	g(x) = integral from 1 to x of natural log of 1+t^2 with respect to t	$g (x) = \int_{1}^{x} \ln (1 + t^{2}) d t$
83851	Find the Derivative - d/dx	cos(x)-csc(x)	$\cos (x) - \csc (x)$
83852	Find the Maximum/Minimum Value	x^3+1	$x^{3} + 1$
83853	Find dv/dh	v=pir^2h	$v = π r^{2} h$
83854	Find the Local Maxima and Minima	f(x)=2/5x^5+5x^4+16x^3-15	$f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15$
83855	Evaluate the Integral	integral from 0 to 1 of x/( square root of x+1) with respect to x	$\int_{0}^{1} \frac{x}{\sqrt{x + 1}} d x$
83856	Evaluate the Limit	limit as x approaches infinity of 10/(6x)	$lim_{x \to \infty} \frac{10}{6 x}$
83857	Evaluate the Integral	integral from -2 to 0 of (1/2t^4+1/4t^3-t) with respect to t	$\int_{- 2}^{0} (\frac{1}{2} t^{4} + \frac{1}{4} t^{3} - t) d t$
83858	Integrate Using u-Substitution	integral from 0 to 2 of x/( square root of 1+2x^2) with respect to x	$\int_{0}^{2} \frac{x}{\sqrt{1 + 2 x^{2}}} d x$
83859	Find the Slope	-2x+3	$- 2 x + 3$
83860	Find Where Increasing/Decreasing	f(x)=2^(x-1)	$f (x) = 2^{x - 1}$
83861	Find dy/dx	y=1/( sixth root of x^2-5x)	$y = \frac{1}{\sqrt[6]{x^{2} - 5 x}}$
83862	Find the Derivative - d/dx	(sin(x)^2)/(1+cos(x))	$\frac{\sin^{2} (x)}{1 + \cos (x)}$
83863	Evaluate the Limit	limit as x approaches 6 of (2 square root of 6 square root of x-12)/(x-6)	$lim_{x \to 6} \frac{2 \sqrt{6} \sqrt{x} - 12}{x - 6}$
83864	Evaluate the Integral	integral of ( square root of x-2x^5+1)/(x^2) with respect to x	$\int \frac{\sqrt{x} - 2 x^{5} + 1}{x^{2}} d x$
83865	Evaluate the Integral	integral of ((x-3)/(x+3)) with respect to x	$\int (\frac{x - 3}{x + 3}) d x$
83866	Evaluate the Limit	limit as x approaches 0 of (9x^2+4x^5)/(-7x^2)	$lim_{x \to 0} \frac{9 x^{2} + 4 x^{5}}{- 7 x^{2}}$
83867	Find the Antiderivative	f(x)=x^2-3x+1/x	$f (x) = x^{2} - 3 x + \frac{1}{x}$
83868	Find the Derivative - d/dx	5x^2* natural log of x	$5 x^{2} \cdot \ln (x)$
83869	Find the Derivative - d/dx	yx^(y-1)	$y x^{y - 1}$
83870	Find dy/dx	y=5 square root of x^2+9	$y = 5 \sqrt{x^{2} + 9}$
83871	Integrate Using u-Substitution	integral of 2x square root of x^2+1 with respect to x	$\int 2 x \sqrt{x^{2} + 1} d x$
83872	Find the Derivative - d/dt	e^(cos(t))	$e^{\cos (t)}$
83873	Find the Second Derivative	y=x^x	$y = x^{x}$
83874	Find the Maximum/Minimum Value	f(x) = square root of 5x+18	$f (x) = \sqrt{5 x + 18}$
83875	Find Where Increasing/Decreasing	f(x)=4-45x+3x^2+x^3	$f (x) = 4 - 45 x + 3 x^{2} + x^{3}$
83876	Find the Antiderivative	x^5-9x^2+4x-1	$x^{5} - 9 x^{2} + 4 x - 1$
83877	Find the Derivative - d/dx	xarcsin(x)+ square root of 1-x^2	$x \arcsin (x) + \sqrt{1 - x^{2}}$
83878	Evaluate the Integral	integral of (2x^3+4x^2-5)/(x+3) with respect to x	$\int \frac{2 x^{3} + 4 x^{2} - 5}{x + 3} d x$
83879	Integrate Using u-Substitution	integral of xcos(x) with respect to x	$\int x \cos (x) d x$
83880	Find the Antiderivative	1/(x square root of x^2+1)	$\frac{1}{x \sqrt{x^{2} + 1}}$
83881	Find the Derivative - d/dy	6tan(3y+1)	$6 \tan (3 y + 1)$
83882	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (5-5x^2)/(4tan(3x-3))	$lim_{x \to 1} \frac{5 - 5 x^{2}}{4 \tan (3 x - 3)}$
83883	Find dy/dx	y=x^2e^x-xe^x	$y = x^{2} e^{x} - x e^{x}$
83884	Find the Derivative - d/dx	1/2tan(x)^2	$\frac{1}{2} \tan^{2} (x)$
83885	Integrate Using u-Substitution	integral from 0 to 3 of square root of y+1 with respect to y	$\int_{0}^{3} \sqrt{y + 1} d y$
83886	Find the Antiderivative	5/((2-8x)^3)	$\frac{5}{{(2 - 8 x)}^{3}}$
83887	Find the Antiderivative	f(x)=1/(cos(3x)^2)	$f (x) = \frac{1}{\cos^{2} (3 x)}$
83888	Evaluate the Integral	integral of x/((1+4x)^2) with respect to x	$\int \frac{x}{{(1 + 4 x)}^{2}} d x$
83889	Evaluate the Integral	integral of (-6-4x^5+x^4) with respect to x	$\int (- 6 - 4 x^{5} + x^{4}) d x$
83890	Find the Derivative - d/dx	y=2x^10-x^6+5x^2	$y = 2 x^{10} - x^{6} + 5 x^{2}$
83891	Evaluate the Limit	limit as x approaches 0 of (2x^2+7x+6)/((x-4)^2)	$lim_{x \to 0} \frac{2 x^{2} + 7 x + 6}{{(x - 4)}^{2}}$
83892	Evaluate the Integral	integral of (3e^x-5x) with respect to x	$\int (3 e^{x} - 5 x) d x$
83893	Evaluate the Integral	integral of t(3t^3+1) with respect to x	$\int t (3 t^{3} + 1) d x$
83894	Find the Derivative - d/dt	y = natural log of 2t^4e^(-t)	$y = \ln (2 t^{4} e^{- t})$
83895	Find the Derivative - d/dx	-2xe^(-x)+2e^(-x)	$- 2 x e^{- x} + 2 e^{- x}$
83896	Evaluate the Integral	integral of (a+bx^2)/( square root of 3ax+bx^3) with respect to a	$\int \frac{a + b x^{2}}{\sqrt{3 a x + b x^{3}}} d a$
83897	Evaluate the Integral	integral from -1 to 1 of e^x-(x^2-1) with respect to x	$\int_{- 1}^{1} e^{x} - (x^{2} - 1) d x$
83898	Find dy/dx	5x^3=y^3-4y	$5 x^{3} = y^{3} - 4 y$
83899	Evaluate the Integral	integral of 2 square root of x square root of 1+(1/( square root of x))^2 with respect to x	$\int 2 \sqrt{x} \sqrt{1 + {(\frac{1}{\sqrt{x}})}^{2}} d x$
83900	Find the Maximum/Minimum Value	f(x)=x^5-4x^3+x^2+2	$f (x) = x^{5} - 4 x^{3} + x^{2} + 2$