Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68201	Find dy/dx	y=e^(3 square root of x)	$y = e^{3 \sqrt{x}}$
68202	Evaluate the Integral	integral from 0 to 1 of (x^e+e^x) with respect to x	$\int_{0}^{1} (x^{e} + e^{x}) d x$
68203	Find the Derivative Using Chain Rule - d/dθ	y=cot(sin(theta))^2	$y = \cot^{2} (\sin (θ))$
68204	Evaluate the Integral	integral of (w^3+w^2+w)/(w^3) with respect to w	$\int \frac{w^{3} + w^{2} + w}{w^{3}} d w$
68205	Find the Area Between the Curves	f(x)=x^2 yf(x)=9	$f (x) = x^{2}$ $y f (x) = 9$
68206	Find dy/dx	y=xcos(x)	$y = x \cos (x)$
68207	Evaluate the Limit	limit as x approaches pi/3 of (-4cos(-x))/(3-2sin(-2x))	$lim_{x \to \frac{π}{3}} \frac{- 4 \cos (- x)}{3 - 2 \sin (- 2 x)}$
68208	Find dy/dx	y = square root of x natural log of x	$y = \sqrt{x} \ln (x)$
68209	Find the Inflection Points	x^(1/3)(x+3)^(2/3)	$x^{\frac{1}{3}} {(x + 3)}^{\frac{2}{3}}$
68210	Find dy/dx	xy^2-x^3y=6	$x y^{2} - x^{3} y = 6$
68211	Integrate By Parts	integral of xcos(5x) with respect to x	$\int x \cos (5 x) d x$
68212	Evaluate the Limit	limit as x approaches 1 of (x+3)/2	$lim_{x \to 1} \frac{x + 3}{2}$
68213	Find dx/dy	y=e^(2x)	$y = e^{2 x}$
68214	Find the Antiderivative	-1/x+C	$- \frac{1}{x} + C$
68215	Find dy/dx	y=x/(x^2+1)	$y = \frac{x}{x^{2} + 1}$
68216	Find dx/dy	x^3+y^3=3xy	$x^{3} + y^{3} = 3 x y$
68217	Find dy/dx	y = natural log of x^2	$y = \ln (x^{2})$
68218	Find the Derivative - d/dx	7^( square root of x)	$7^{\sqrt{x}}$
68219	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(e^x-1)	$lim_{x \to 0} \frac{\sin (x)}{e^{x} - 1}$
68220	Find dy/dx	sin(x^2+y^2)=xe^y	$\sin (x^{2} + y^{2}) = x e^{y}$
68221	Find dy/dx	y=x^-10	$y = x^{- 10}$
68222	Find the Derivative - d/dx	d/(dx)x^x	$\frac{d}{d x} x^{x}$
68223	Evaluate the Integral	integral from -5 to 2 of (x^2+3x-10) with respect to x	$\int_{- 5}^{2} (x^{2} + 3 x - 10) d x$
68224	Solve the Differential Equation	(dy)/(dx)=xy	$\frac{d y}{d x} = x y$
68225	Find the Derivative - d/dx	(1+x^2)^-1	${(1 + x^{2})}^{- 1}$
68226	Find the Integral	1/(x^3)dx	$\frac{1}{x^{3}} d x$
68227	Evaluate the Integral	integral from 3 to 1 of (3x-2) with respect to x	$\int_{3}^{1} (3 x - 2) d x$
68228	Evaluate the Limit	limit as x approaches infinity of (2x-7)/(x^2+x+3)	$lim_{x \to \infty} \frac{2 x - 7}{x^{2} + x + 3}$
68229	Find dx/dy	x^2+xy+y^2=3	$x^{2} + x y + y^{2} = 3$
68230	Evaluate the Integral	integral of e^(-st) with respect to s	$\int e^{- s t} d s$
68231	Find the Derivative - d/dx	y=- square root of x	$y = - \sqrt{x}$
68232	Evaluate the Integral	integral of (3/x+2e^x) with respect to x	$\int (\frac{3}{x} + 2 e^{x}) d x$
68233	Evaluate the Integral	integral from 1 to 2 of (x^2-3) with respect to x	$\int_{1}^{2} (x^{2} - 3) d x$
68234	Find the Derivative - d/dx	1/( square root of x^2+y^2+z^2)	$\frac{1}{\sqrt{x^{2} + y^{2} + z^{2}}}$
68235	Find dy/dx	y=4/x	$y = \frac{4}{x}$
68236	Find the Tangent Line at (1,1)	f(x) = square root of x , (1,1)	$f (x) = \sqrt{x}$ , $(1, 1)$
68237	Find the Derivative - d/dx	y=(8x)/(e^x)	$y = \frac{8 x}{e^{x}}$
68238	Find the Derivative - d/dx	(5-x)/(x^3+2)	$\frac{5 - x}{x^{3} + 2}$
68239	Find the Maximum/Minimum Value	k(x)=6x^4+8x^3	$k (x) = 6 x^{4} + 8 x^{3}$
68240	Find dy/dx	y=arcsin(6x+1)	$y = \arcsin (6 x + 1)$
68241	Find dy/dx	x^2y-4x^2=0	$x^{2} y - 4 x^{2} = 0$
68242	Find the Derivative - d/dx	e^(tan(x)^2)	$e^{\tan^{2} (x)}$
68243	Find the Integral	f(x)=2x	$f (x) = 2 x$
68244	Find the Derivative - d/dx	1/2 natural log of x	$\frac{1}{2} \ln (x)$
68245	Find dy/dx	x^2y-3x^3+8=0	$x^{2} y - 3 x^{3} + 8 = 0$
68246	Find dy/dx	xsin(y)+ysin(x)=3	$x \sin (y) + y \sin (x) = 3$
68247	Find Where Increasing/Decreasing	f(x)=(x-1)^3-12x	$f (x) = {(x - 1)}^{3} - 12 x$
68248	Integrate Using u-Substitution	integral of x^3 square root of x^2+1 with respect to x	$\int x^{3} \sqrt{x^{2} + 1} d x$
68249	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( natural log of 5x)/( square root of 5x)	$lim_{x \to \infty} \frac{\ln (5 x)}{\sqrt{5 x}}$
68250	Find dy/dx	x^3+y^3=16xy-3	$x^{3} + y^{3} = 16 x y - 3$
68251	Find the Maximum/Minimum Value	y=x square root of 4-x^2	$y = x \sqrt{4 - x^{2}}$
68252	Find the Inflection Points	f(x)=x^(1/3)(x+3)^(2/3)	$f (x) = x^{\frac{1}{3}} {(x + 3)}^{\frac{2}{3}}$
68253	Evaluate the Integral	integral of (3x^4+x^2+2) with respect to x	$\int (3 x^{4} + x^{2} + 2) d x$
68254	Find dy/dx	square root of x+y=1+x^2y^2	$\sqrt{x + y} = 1 + x^{2} y^{2}$
68255	Find dy/dx	x^2+y^2=169	$x^{2} + y^{2} = 169$
68256	Find dy/dx	x^3+y^3=9xy	$x^{3} + y^{3} = 9 x y$
68257	Find the Center and Radius	(x^2)/16-(y^2)/9=1	$\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$
68258	Find the Derivative - d/dx	d/(dx)x^( square root of x)	$\frac{d}{d x} x^{\sqrt{x}}$
68259	Find the Absolute Max and Min over the Interval	f(x)=3sin(x)+3cos(x) , 0<=x<=2pi	$f (x) = 3 \sin (x) + 3 \cos (x)$ , $0 \leq x \leq 2 π$
68260	Find dx/dy	x^2+y^2=100	$x^{2} + y^{2} = 100$
68261	Find the Tangent Line at (π/3,2)	y=sec(x) , (pi/3,2)	$y = \sec (x)$ , $(\frac{π}{3}, 2)$
68262	Find dy/dx	y=sec(x)^2	$y = \sec^{2} (x)$
68263	Evaluate the Integral	integral of ( square root of x+1/( square root of x)) with respect to x	$\int (\sqrt{x} + \frac{1}{\sqrt{x}}) d x$
68264	Find the Derivative - d/dx	(4-x^(2/3))^(3/2)	${(4 - x^{\frac{2}{3}})}^{\frac{3}{2}}$
68265	Find the Derivative - d/dx	2(x^2+y^2)^2=25(x^2-y^2)	$2 {(x^{2} + y^{2})}^{2} = 25 (x^{2} - y^{2})$
68266	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of tan(7x)^x	$lim_{x \to 0^{+}} {\tan (7 x)}^{x}$
68267	Find dy/dx	y=arcsin(8x+1)	$y = \arcsin (8 x + 1)$
68268	Find the Derivative - d/dx	y=2x^2 square root of 2-x	$y = 2 x^{2} \sqrt{2 - x}$
68269	Find the Derivative - d/dx	d/(dx)(cos(x)-7x)	$\frac{d}{d x} (\cos (x) - 7 x)$
68270	Find dx/dy	y = cube root of x	$y = \sqrt[3]{x}$
68271	Find the Derivative - d/dX	square root of 49-X^2	$\sqrt{49 - X^{2}}$
68272	Find the Domain and Range	f(x)=-x+3 if x<1; 4x-2 if x>=1	$f (x) = {\begin{cases} - x + 3 & x < 1 \\ 4 x - 2 & x \geq 1 \end{cases}$
68273	Find dy/dx	y=3/x	$y = \frac{3}{x}$
68274	Evaluate the Integral	integral from 1 to 4 of (4+x^2)/( square root of x) with respect to x	$\int_{1}^{4} \frac{4 + x^{2}}{\sqrt{x}} d x$
68275	Find the Derivative - d/dx	(2x^2-1)/(5x+3)	$\frac{2 x^{2} - 1}{5 x + 3}$
68276	Find Where Increasing/Decreasing	f(x)=x^6e^(-x)	$f (x) = x^{6} e^{- x}$
68277	Find the Derivative - d/dx	y=6 square root of 10-x^5	$y = 6 \sqrt{10 - x^{5}}$
68278	Evaluate the Limit	limit as x approaches 3/2 of (4x^2-9)/(2x+3)	$lim_{x \to \frac{3}{2}} \frac{4 x^{2} - 9}{2 x + 3}$
68279	Evaluate the Integral	integral from -1 to 2 of (x^3-2x) with respect to x	$\int_{- 1}^{2} (x^{3} - 2 x) d x$
68280	Integrate Using Trig Substitution	integral of ( square root of x^2-9)/(x^3) with respect to x	$\int \frac{\sqrt{x^{2} - 9}}{x^{3}} d x$
68281	Evaluate the Limit	limit as x approaches -1/3 of (x^2+1/9)(x-1/3)	$lim_{x \to - \frac{1}{3}} (x^{2} + \frac{1}{9}) (x - \frac{1}{3})$
68282	Find dy/dx	y=e^(4x)	$y = e^{4 x}$
68283	Evaluate the Integral	integral from 2 to 5 of (x^2+2x) with respect to x	$\int_{2}^{5} (x^{2} + 2 x) d x$
68284	Find the Derivative - d/dx	sec(x)-x	$\sec (x) - x$
68285	Find dy/dx	y=xe^(-x)	$y = x e^{- x}$
68286	Find the Derivative - d/dy	xyz	$x y z$
68287	Evaluate the Integral	integral of (x^2-3x+2) with respect to x	$\int (x^{2} - 3 x + 2) d x$
68288	Find the Derivative - d/dx	2/(x^3)-1/(x^2)	$\frac{2}{x^{3}} - \frac{1}{x^{2}}$
68289	Find dy/dx	y = natural log of cos(x)	$y = \ln (\cos (x))$
68290	Find the Derivative - d/dx	(1-cos(x))/(sin(x))	$\frac{1 - \cos (x)}{\sin (x)}$
68291	Find the Slope	-4/3	$- \frac{4}{3}$
68292	Find the Antiderivative	cos(x)^4	$\cos^{4} (x)$
68293	Find the Derivative - d/dx	d/(dx)(1/(x^4)+1/(x^2)-x^3)	$\frac{d}{d x} (\frac{1}{x^{4}} + \frac{1}{x^{2}} - x^{3})$
68294	Find the Domain and Range	f(x)=-x+4 if x<1; 4x-1 if x>=1	$f (x) = {\begin{cases} - x + 4 & x < 1 \\ 4 x - 1 & x \geq 1 \end{cases}$
68295	Find the Derivative - d/dx	y=x^4(5x-4x^2)	$y = x^{4} (5 x - 4 x^{2})$
68296	Find the Derivative - d/dx	d/(dx)( square root of x^5)	$\frac{d}{d x} (\sqrt{x^{5}})$
68297	Find dy/dx	sin(x+y)=2x-2y	$\sin (x + y) = 2 x - 2 y$
68298	Evaluate the Limit	limit as x approaches -3 of ( square root of -x-1- square root of 2)/(-x-3)	$lim_{x \to - 3} \frac{\sqrt{- x - 1} - \sqrt{2}}{- x - 3}$
68299	Integrate Using u-Substitution	integral of x square root of x-1 with respect to x	$\int x \sqrt{x - 1} d x$
68300	Find the Derivative - d/dx	d/(dx)(csc(x))	$\frac{d}{d x} (\csc (x))$