Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67701	Find the Antiderivative	3^(2x)	$3^{2 x}$
67702	Find the Antiderivative	f(x)=20x^4-4x^3+15x^2-14x-9	$f (x) = 20 x^{4} - 4 x^{3} + 15 x^{2} - 14 x - 9$
67703	Find the Derivative - d/dt	square root of 2t	$\sqrt{2 t}$
67704	Integrate Using Partial Fractions	integral of 1/(x^2-4) with respect to x	$\int \frac{1}{x^{2} - 4} d x$
67705	Find the Derivative - d/dx	y=2 square root of x-1/(2 square root of x)	$y = 2 \sqrt{x} - \frac{1}{2 \sqrt{x}}$
67706	Evaluate the Integral	integral from 1 to 3 of (1/(x^2)-6/(x^3)) with respect to x	$\int_{1}^{3} (\frac{1}{x^{2}} - \frac{6}{x^{3}}) d x$
67707	Evaluate the Integral	integral from -4 to 1 of (3x+6) with respect to x	$\int_{- 4}^{1} (3 x + 6) d x$
67708	Find dy/dx	(x-y)^2=x+y-1	${(x - y)}^{2} = x + y - 1$
67709	Evaluate the Integral	integral of (5/( cube root of x)-4 cube root of x) with respect to x	$\int (\frac{5}{\sqrt[3]{x}} - 4 \sqrt[3]{x}) d x$
67710	Integrate Using Trig Substitution	integral of ( square root of x^2-4)/x with respect to x	$\int \frac{\sqrt{x^{2} - 4}}{x} d x$
67711	Find Where Increasing/Decreasing	f(x)=2x	$f (x) = 2 x$
67712	Find the Derivative - d/dx	square root of 1	$\sqrt{1}$
67713	Find the Derivative - d/dx	f(5)	$f (5)$
67714	Find dy/dx	x^2+xy+y^2=1	$x^{2} + x y + y^{2} = 1$
67715	Integrate By Parts	integral of arctan(x) with respect to x	$\int \arctan (x) d x$
67716	Find dy/dx	y=cos(x)^x	$y = {\cos (x)}^{x}$
67717	Find the Derivative - d/dy	square root of x^2+y^2+z^2	$\sqrt{x^{2} + y^{2} + z^{2}}$
67718	Find dy/dx	e^(2y)-e^(y^2-y)=x^4-x^2	$e^{2 y} - e^{y^{2} - y} = x^{4} - x^{2}$
67719	Find the Second Derivative	(d^2)/(dx^2)(sin(x)+cos(x))	$\frac{d^{2}}{d x^{2}} (\sin (x) + \cos (x))$
67720	Find the Derivative - d/dx	(e^x)/( square root of x)	$\frac{e^{x}}{\sqrt{x}}$
67721	Find the Derivative - d/dx	1/2e^(2x)	$\frac{1}{2} e^{2 x}$
67722	Find the Derivative - d/dx	natural log of x+4+e^(-3x)	$\ln (x + 4 + e^{- 3 x})$
67723	Find the Third Derivative	f(x)=x square root of x^2+1	$f (x) = x \sqrt{x^{2} + 1}$
67724	Find dy/dx	tan(2x+y)=2x	$\tan (2 x + y) = 2 x$
67725	Find the Derivative - d/dx	1/2(e^x+e^(-x))	$\frac{1}{2} (e^{x} + e^{- x})$
67726	Find dy/dx	y=7x	$y = 7 x$
67727	Find the Center and Radius	(x+3)^2-49=-y^2	${(x + 3)}^{2} - 49 = - y^{2}$
67728	Evaluate the Limit	limit as x approaches 0 from the right of (1+1/x)^x	$lim_{x \to 0^{+}} {(1 + \frac{1}{x})}^{x}$
67729	Find the Derivative - d/dx	d/(dx)(2cos(x)-3 natural log of x-1)	$\frac{d}{d x} (2 \cos (x) - 3 \ln (x) - 1)$
67730	Evaluate the Limit	limit as x approaches 0 of (sin(x))/x=1	$lim_{x \to 0} \frac{\sin (x)}{x} = 1$
67731	Find dy/dx	square root of x+y=3x	$\sqrt{x + y} = 3 x$
67732	Find the Antiderivative	xsin(x)	$x \sin (x)$
67733	Find dx/dy	y=1/(x^2)	$y = \frac{1}{x^{2}}$
67734	Find dy/dx	y=4 square root of x	$y = 4 \sqrt{x}$
67735	Find the Arc Length	y = square root of 2-x^2 , 0<=x<=1	$y = \sqrt{2 - x^{2}}$ , $0 \leq x \leq 1$
67736	Find the Derivative - d/dx	x^2dx	$x^{2} d x$
67737	Find the Slope	0	$0$
67738	Find dx/dy	xy=4	$x y = 4$
67739	Find the Derivative - d/dx	cos(e^x)	$\cos (e^{x})$
67740	Find dy/dx	x^2+4xy+8y^2=20	$x^{2} + 4 x y + 8 y^{2} = 20$
67741	Find dy/dx	y=e^(x^3)	$y = e^{x^{3}}$
67742	Find the Derivative - d/dy	(2x)/y	$\frac{2 x}{y}$
67743	Find the Derivative - d/dx	(sin(x)^2)	$(\sin^{2} (x))$
67744	Find the Derivative - d/dx	e^xsin(y)	$e^{x} \sin (y)$
67745	Determine if Continuous	f(x)=1+x^2 if x<1; 9x-7 if x>=1	$f (x) = {\begin{cases} 1 + x^{2} & x < 1 \\ 9 x - 7 & x \geq 1 \end{cases}$
67746	Find dy/dx	y=2x^3	$y = 2 x^{3}$
67747	Evaluate the Limit	limit as x approaches 0 from the left of x/(\|x\|)	$lim_{x \to 0^{-}} \frac{x}{\| x \|}$
67748	Evaluate the Integral	integral of (x^5+1) with respect to x	$\int (x^{5} + 1) d x$
67749	Evaluate the Limit	limit as x approaches 0 of x/(1- square root of 1-x)	$lim_{x \to 0} \frac{x}{1 - \sqrt{1 - x}}$
67750	Find dx/dy	xy=1	$x y = 1$
67751	Evaluate the Integral	integral from -1 to 1 of ( cube root of t-2) with respect to t	$\int_{- 1}^{1} (\sqrt[3]{t} - 2) d t$
67752	Evaluate the Integral	integral from 0 to 0.75 of (x^2)/( square root of 9-16x^2) with respect to x	$\int_{0}^{0.75} \frac{x^{2}}{\sqrt{9 - 16 x^{2}}} d x$
67753	Find the Derivative - d/dx	d/(dx)sec(x)^2	$\frac{d}{d x} \sec^{2} (x)$
67754	Evaluate the Integral	integral of 5x square root of 1+4x^2 with respect to x	$\int 5 x \sqrt{1 + 4 x^{2}} d x$
67755	Find dy/dx	tan(x/y)=x+y	$\tan (\frac{x}{y}) = x + y$
67756	Evaluate the Limit	limit as x approaches 0 of (tan(2x))/(6xsec(3x))	$lim_{x \to 0} \frac{\tan (2 x)}{6 x \sec (3 x)}$
67757	Evaluate the Limit	limit as x approaches 0 of (1-cos(x))/(sin(x)^2)	$lim_{x \to 0} \frac{1 - \cos (x)}{\sin^{2} (x)}$
67758	Evaluate the Integral	integral from 0 to 1 of x natural log of x with respect to x	$\int_{0}^{1} x \ln (x) d x$
67759	Find dy/dx	y^3-xy^2+x^3=5	$y^{3} - x y^{2} + x^{3} = 5$
67760	Find the Derivative - d/dx	2/(3x^(1/3))	$\frac{2}{3 x^{\frac{1}{3}}}$
67761	Evaluate the Limit	limit as x approaches 1 of natural log of (7-x^2)/(1+x)	$lim_{x \to 1} \ln (\frac{7 - x^{2}}{1 + x})$
67762	Find dy/dx	y=1/(x^5)	$y = \frac{1}{x^{5}}$
67763	Find dy/dx	y=x natural log of x	$y = x \ln (x)$
67764	Evaluate the Integral	integral from 0 to 1/( square root of 3) of 4(t^2-1)/(t^4-1) with respect to t	$\int_{0}^{\frac{1}{\sqrt{3}}} 4 \frac{t^{2} - 1}{t^{4} - 1} d t$
67765	Find dx/dy	x^2-8xy+y^2=8	$x^{2} - 8 x y + y^{2} = 8$
67766	Find the Derivative - d/dx	x+ square root of 4-x^2	$x + \sqrt{4 - x^{2}}$
67767	Find the Maximum/Minimum Value	f(x)=a(x-h)^2+k	$f (x) = a {(x - h)}^{2} + k$
67768	Find the Derivative - d/dr	A=pir^2	$A = π r^{2}$
67769	Integrate By Parts	integral of natural log of square root of x with respect to x	$\int \ln (\sqrt{x}) d x$
67770	Find the Integral	x natural log of x	$x \ln (x)$
67771	Evaluate the Integral	e^( integral of 2/x with respect to x)	$e^{\int \frac{2}{x} d x}$
67772	Find the Derivative - d/dx	1/xe^x	$\frac{1}{x} e^{x}$
67773	Find dy/dx	y = square root of 4-x^2	$y = \sqrt{4 - x^{2}}$
67774	Find the Derivative - d/dx	d/(dx)(xy)	$\frac{d}{d x} (x y)$
67775	Find the Maximum/Minimum Value	y=x^2+x	$y = x^{2} + x$
67776	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x+e^(-x)-2)/(e^x-x-1)	$lim_{x \to 0} \frac{e^{x} + e^{- x} - 2}{e^{x} - x - 1}$
67777	Evaluate the Limit	limit as x approaches 1 of ( cube root of x-1)/( fourth root of x-1)	$lim_{x \to 1} \frac{\sqrt[3]{x} - 1}{\sqrt[4]{x} - 1}$
67778	Find dy/dx	y^2(y^2-4)=x^2(x^2-5)	$y^{2} (y^{2} - 4) = x^{2} (x^{2} - 5)$
67779	Find dy/dx	2y+6x=3x^2-y^4	$2 y + 6 x = 3 x^{2} - y^{4}$
67780	Evaluate the Limit	limit as x approaches 4 from the left of ( square root of x-2)/(x-4)	$lim_{x \to 4^{-}} \frac{\sqrt{x} - 2}{x - 4}$
67781	Find the Derivative - d/dx	e^(y/x)	$e^{\frac{y}{x}}$
67782	Find the Derivative - d/dx	y=ax square root of b	$y = a x \sqrt{b}$
67783	Find dy/dx	2x^2+xy-y^2=2	$2 x^{2} + x y - y^{2} = 2$
67784	Find the Slope	5	$5$
67785	Find the Derivative - d/dθ	theta^2sin(theta)	$θ^{2} \sin (θ)$
67786	Evaluate the Integral	integral from -1 to 1 of (x+2x^2-x^3+5x^4) with respect to x	$\int_{- 1}^{1} (x + 2 x^{2} - x^{3} + 5 x^{4}) d x$
67787	Find dy/dx	y=x^5	$y = x^{5}$
67788	Find Where Increasing/Decreasing	f(x)=(x^2)/(x^2-1)	$f (x) = \frac{x^{2}}{x^{2} - 1}$
67789	Find dy/dx	(4-x)y^2=x^3	$(4 - x) y^{2} = x^{3}$
67790	Find dy/dx	y=(x+1)/(x-1)	$y = \frac{x + 1}{x - 1}$
67791	Find dy/dx	y^2=x^3+3x^2	$y^{2} = x^{3} + 3 x^{2}$
67792	Find the Derivative - d/dx	y=tan(2x)^3	$y = \tan^{3} (2 x)$
67793	Evaluate the Limit	limit as x approaches infinity of x/( square root of x^2-x)	$lim_{x \to \infty} \frac{x}{\sqrt{x^{2} - x}}$
67794	Integrate Using Trig Substitution	integral of ( square root of 4-x^2)/(x^2) with respect to x	$\int \frac{\sqrt{4 - x^{2}}}{x^{2}} d x$
67795	Find dy/dx	y=(e^x-e^(-x))/(e^x+e^(-x))	$y = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$
67796	Find the Integral	3x^2dx	$3 x^{2} d x$
67797	Find the Derivative - d/dx	d/(dx)cos(x)^2	$\frac{d}{d x} \cos^{2} (x)$
67798	Find the Derivative - d/dy	xcos(y)	$x \cos (y)$
67799	Find the Derivative - d/dx	(1-x)	$(1 - x)$
67800	Evaluate the Limit	limit as x approaches 6 of (5 square root of x+3)/(4x^2)	$lim_{x \to 6} \frac{5 \sqrt{x} + 3}{4 x^{2}}$