Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69601	Find the Derivative - d/dh	limit as h approaches 0 of (cos(pi+h)+1)/h	$lim_{h \to 0} \frac{\cos (π + h) + 1}{h}$
69602	Find dy/dx	y=sin(x)^2+cos(x)^2	$y = \sin^{2} (x) + \cos^{2} (x)$
69603	Find dx/dy	y=xsin(x)	$y = x \sin (x)$
69604	Evaluate the Integral	integral from 0 to 1 of ( square root of x-x^2) with respect to x	$\int_{0}^{1} (\sqrt{x} - x^{2}) d x$
69605	Find the Tangent Line at (1,e)	y=x^2e^x-2xe^x+2e^x , (1,e)	$y = x^{2} e^{x} - 2 x e^{x} + 2 e^{x}$ , $(1, e)$
69606	Integrate By Parts	integral of x square root of 1+x with respect to x	$\int x \sqrt{1 + x} d x$
69607	Find the Derivative - d/dt	y=ccos(t)+t^2sin(t)	$y = c \cos (t) + t^{2} \sin (t)$
69608	Find the Derivative - d/dx	y=1/(3x^2+1)	$y = \frac{1}{3 x^{2} + 1}$
69609	Evaluate the Limit	limit as x approaches 0 of (sin(x)cos(4x))/(x+xcos(5x))	$lim_{x \to 0} \frac{\sin (x) \cos (4 x)}{x + x \cos (5 x)}$
69610	Find dy/dx	y=e^(x/10)	$y = e^{\frac{x}{10}}$
69611	Evaluate the Integral	integral from -4 to 4 of (3x^2-10) with respect to x	$\int_{- 4}^{4} (3 x^{2} - 10) d x$
69612	Integrate By Parts	integral of x^2e^(4x) with respect to x	$\int x^{2} e^{4 x} d x$
69613	Find the Derivative - d/dx	x-pi	$x - π$
69614	Integrate By Parts	integral of x^3cos(x) with respect to x	$\int x^{3} \cos (x) d x$
69615	Find the Derivative - d/dx	cosh( natural log of x)	$\cosh (\ln (x))$
69616	Solve the Differential Equation	(dy)/(dx)+y=e^(3x)	$\frac{d y}{d x} + y = e^{3 x}$
69617	Find the Tangent Line at (4,0)	y = natural log of x^2-4x+1 , (4,0)	$y = \ln (x^{2} - 4 x + 1)$ , $(4, 0)$
69618	Find the Maximum/Minimum Value	y=-(x-3)^2+a	$y = - {(x - 3)}^{2} + a$
69619	Evaluate the Limit	limit as h approaches 0 of (3(2+h)^4-3(2)^4)/h	$lim_{h \to 0} \frac{3 {(2 + h)}^{4} - 3 {(2)}^{4}}{h}$
69620	Find the Derivative - d/dX	3/(2 square root of X)	$\frac{3}{2 \sqrt{X}}$
69621	Find dy/dx	x^2y-4x=5	$x^{2} y - 4 x = 5$
69622	Find the Center and Radius	(x^2)/63500+(y^2)/50900=1	$\frac{x^{2}}{63500} + \frac{y^{2}}{50900} = 1$
69623	Find the Derivative - d/dx	3x^2e^(x^3)	$3 x^{2} e^{x^{3}}$
69624	Evaluate the Integral	integral of x( square root of x-1) with respect to x	$\int x (\sqrt{x} - 1) d x$
69625	Find the Tangent Line at (2,0)	y = natural log of x^2-2x+1 , (2,0)	$y = \ln (x^{2} - 2 x + 1)$ , $(2, 0)$
69626	Find the Derivative - d/dx	(2x)/(1-x^2)	$\frac{2 x}{1 - x^{2}}$
69627	Evaluate the Integral	integral of (csc(x)+tan(x))^2 with respect to x	$\int {(\csc (x) + \tan (x))}^{2} d x$
69628	Evaluate the Limit	limit as x approaches 3 of (2x^3-6x^2+x-3)/(x-3)	$lim_{x \to 3} \frac{2 x^{3} - 6 x^{2} + x - 3}{x - 3}$
69629	Find dy/dx	x^2y^2+xsin(y)=4	$x^{2} y^{2} + x \sin (y) = 4$
69630	Solve the Differential Equation	(dy)/(dx)=2x	$\frac{d y}{d x} = 2 x$
69631	Find the Inflection Points	F(x)=x square root of 6-x	$F (x) = x \sqrt{6 - x}$
69632	Find the Derivative - d/dx	e^x(-x^(2/3)-4/3x^(-3/2))	$e^{x} (- x^{\frac{2}{3}} - \frac{4}{3} x^{- \frac{3}{2}})$
69633	Find the Derivative - d/dx	y=4 square root of x-6/( cube root of x^2)	$y = 4 \sqrt{x} - \frac{6}{\sqrt[3]{x^{2}}}$
69634	Evaluate the Integral	integral of (8/x-5/(x^2)+6/(x^3)) with respect to x	$\int (\frac{8}{x} - \frac{5}{x^{2}} + \frac{6}{x^{3}}) d x$
69635	Find Where Increasing/Decreasing	f(x)=x/(x+1)	$f (x) = \frac{x}{x + 1}$
69636	Find the Slope	-6	$- 6$
69637	Find the Derivative - d/dx	(x-pi)^2	${(x - π)}^{2}$
69638	Find dy/dx	6x^3+7y^3=13xy	$6 x^{3} + 7 y^{3} = 13 x y$
69639	Find the Derivative - d/dx	-2cos(x)+3x^3	$- 2 \cos (x) + 3 x^{3}$
69640	Find the Tangent Line at (0,7)	y=x^4+7e^x , (0,7)	$y = x^{4} + 7 e^{x}$ , $(0, 7)$
69641	Evaluate the Limit	limit as x approaches infinity of (x^2)/((x-5)(3-x))	$lim_{x \to \infty} \frac{x^{2}}{(x - 5) (3 - x)}$
69642	Find the Derivative - d/dx	1/(csc(x))	$\frac{1}{\csc (x)}$
69643	Find dy/dx	y=x^2cot(x)	$y = x^{2} \cot (x)$
69644	Evaluate the Integral	integral from -1 to 0 of (x-2) with respect to x	$\int_{- 1}^{0} (x - 2) d x$
69645	Find the Third Derivative	f(x)=2cos(x/2)	$f (x) = 2 \cos (\frac{x}{2})$
69646	Find dy/dx	y=(x-2)/(y+3)	$y = \frac{x - 2}{y + 3}$
69647	Find dy/dx	y = square root of x+2	$y = \sqrt{x + 2}$
69648	Find the Derivative - d/dx	y=(a-x)/(a+x)	$y = \frac{a - x}{a + x}$
69649	Evaluate the Integral	integral of (1/x) with respect to x	$\int (\frac{1}{x}) d x$
69650	Find the Tangent Line at (1,5)	y=6x^2-x^3 , (1,5)	$y = 6 x^{2} - x^{3}$ , $(1, 5)$
69651	Evaluate the Limit	limit as x approaches infinity of (-2x^2+5x)/(4x^3-2x+1)	$lim_{x \to \infty} \frac{- 2 x^{2} + 5 x}{4 x^{3} - 2 x + 1}$
69652	Find the Derivative - d/dx	d/(dx)(6/(x^4)+1/(x^2))	$\frac{d}{d x} (\frac{6}{x^{4}} + \frac{1}{x^{2}})$
69653	Evaluate the Integral	integral from 0 to pi of (sin(x)-6) with respect to x	$\int_{0}^{π} (\sin (x) - 6) d x$
69654	Find dt/dy	y=tan( square root of 7t)	$y = \tan (\sqrt{7 t})$
69655	Evaluate the Limit	limit as x approaches 0 of (5x^5+3x^2+18x)/(3x^5+6x)	$lim_{x \to 0} \frac{5 x^{5} + 3 x^{2} + 18 x}{3 x^{5} + 6 x}$
69656	Use Logarithmic Differentiation to Find the Derivative	y=x^(x^2)	$y = x^{x^{2}}$
69657	Find the Derivative - d/dx	y=4x^5+x	$y = 4 x^{5} + x$
69658	Find the Derivative - d/dx	x^2-4/(x^3)	$x^{2} - \frac{4}{x^{3}}$
69659	Find the Maximum/Minimum Value	y=sec(x)	$y = \sec (x)$
69660	Find Where Increasing/Decreasing	f(x)=2/x+x/3	$f (x) = \frac{2}{x} + \frac{x}{3}$
69661	Find the Antiderivative	f''''''''(theta)=sin(theta)+cos(theta)	$f'''' (θ) = \sin (θ) + \cos (θ)$
69662	Find the Derivative - d/dx	d/(dx)(9/(x^3)+1/x)	$\frac{d}{d x} (\frac{9}{x^{3}} + \frac{1}{x})$
69663	Find the Derivative - d/dx	x+ square root of x^2+1	$x + \sqrt{x^{2} + 1}$
69664	Find the Maximum/Minimum Value	C(x)=x^(1/5)(x+6)	$C (x) = x^{\frac{1}{5}} (x + 6)$
69665	Evaluate the Limit	limit as x approaches infinity of (4x-3)/(2x+5)	$lim_{x \to \infty} \frac{4 x - 3}{2 x + 5}$
69666	Find the Derivative - d/dx	d/(dx)((2x+3)/(3x^2-4))	$\frac{d}{d x} (\frac{2 x + 3}{3 x^{2} - 4})$
69667	Integrate Using Trig Substitution	integral of square root of 1-x^2 with respect to x	$\int \sqrt{1 - x^{2}} d x$
69668	Find the Derivative - d/dx	tan(x^2-4x)	$\tan (x^{2} - 4 x)$
69669	Find the Normal Line at (0,3)	y=x^4+3e^x , (0,3)	$y = x^{4} + 3 e^{x}$ , $(0, 3)$
69670	Find Where Increasing/Decreasing	f(x)=3 cube root of -2x+1	$f (x) = 3 \sqrt[3]{- 2 x} + 1$
69671	Evaluate the Integral	integral of 1/(x square root of 9x^2+4) with respect to x	$\int \frac{1}{x \sqrt{9 x^{2} + 4}} d x$
69672	Find dy/dx	y=e^(7x)	$y = e^{7 x}$
69673	Find the Derivative - d/dx	cos(4e^(-8x))	$\cos (4 e^{- 8 x})$
69674	Evaluate the Integral	integral from 0 to pi of (sin(x)-2) with respect to x	$\int_{0}^{π} (\sin (x) - 2) d x$
69675	Find the Tangent Line at (1,2)	y^2=x^3+3x^2 , (1,2)	$y^{2} = x^{3} + 3 x^{2}$ , $(1, 2)$
69676	Evaluate the Limit	limit as x approaches 0 of (1/(-2+x)+1/2)/x	$lim_{x \to 0} \frac{\frac{1}{- 2 + x} + \frac{1}{2}}{x}$
69677	Find the Integral	x^-2dx	$x^{- 2} d x$
69678	Evaluate the Integral	integral from 2 to 4 of 1/((x^2-1)^(3/2)) with respect to x	$\int_{2}^{4} \frac{1}{{(x^{2} - 1)}^{\frac{3}{2}}} d x$
69679	Find dy/dx	(x^2)/4+(y^2)/9=1	$\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$
69680	Evaluate the Summation	sum from i=1 to 5 of (x_i)^2	$\sum_{i = 1}^{5} {(x_{i})}^{2}$
69681	Evaluate the Limit	limit as x approaches infinity of (5x^2+2x-2x^3)/(ax^3+x^2-6)	$lim_{x \to \infty} \frac{5 x^{2} + 2 x - 2 x^{3}}{a x^{3} + x^{2} - 6}$
69682	Evaluate the Limit	limit as x approaches 3 of ( square root of 2x+3-x)/(x-3)	$lim_{x \to 3} \frac{\sqrt{2 x + 3} - x}{x - 3}$
69683	Evaluate the Integral	integral of (x^2+2x)(x+1) with respect to x	$\int (x^{2} + 2 x) (x + 1) d x$
69684	Find the Derivative - d/dx	y = square root of x^-1( square root of x-3/( square root of x))	$y = \sqrt{x^{- 1}} (\sqrt{x} - \frac{3}{\sqrt{x}})$
69685	Find the Derivative - d/dx	fourth root of 16xcos(x)	$\sqrt[4]{16 x} \cos (x)$
69686	Evaluate the Limit	limit as x approaches 0 of (\|x+2\|-2)/(\|x\|)	$lim_{x \to 0} \frac{\| x + 2 \| - 2}{\| x \|}$
69687	Find the Domain and Range	f(x)=\|3x\| if -1<=x<0; x^3 if x>=0	$f (x) = {\begin{cases} \| 3 x \| & - 1 \leq x < 0 \\ x^{3} & x \geq 0 \end{cases}$
69688	Find dy/dx	4x^3y^3=-2y	$4 x^{3} y^{3} = - 2 y$
69689	Find the Derivative - d/dt	s=t^3-27t	$s = t^{3} - 27 t$
69690	Find the Tangent Line at (0,5)	y=x^4+5e^x , (0,5)	$y = x^{4} + 5 e^{x}$ , $(0, 5)$
69691	Find the Derivative - d/dv	u=v+cos(v)	$u = v + \cos (v)$
69692	Evaluate the Summation	sum from k=4 to 9 of -5+k	$\sum_{k = 4}^{9} - 5 + k$
69693	Find the Derivative - d/dx	y=x^3(5x^2-2x+7)	$y = x^{3} (5 x^{2} - 2 x + 7)$
69694	Find the Horizontal Tangent Line	y=x^3+x	$y = x^{3} + x$
69695	Evaluate the Integral	integral of 1/(x^2e^(1/x)) with respect to x	$\int \frac{1}{x^{2} e^{\frac{1}{x}}} d x$
69696	Find dy/dx	y=x^2e^(3x)	$y = x^{2} e^{3 x}$
69697	Find dy/dx	y=(2x-1)^3	$y = {(2 x - 1)}^{3}$
69698	Find the Derivative - d/dx	ye^(-x)	$y e^{- x}$
69699	Find the Derivative - d/dx	y=x/(1-x^3)	$y = \frac{x}{1 - x^{3}}$
69700	Evaluate the Limit	limit as x approaches 1 of square root of 2x^2+x+1	$lim_{x \to 1} \sqrt{2 x^{2} + x + 1}$