Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68301	Find dy/dx	x^2+y^2=(2x^2+2y^2-x)^2	$x^{2} + y^{2} = {(2 x^{2} + 2 y^{2} - x)}^{2}$
68302	Find the Derivative - d/dx	1-tan(x)	$1 - \tan (x)$
68303	Find the Derivative - d/dx	y = square root of 1+x^2	$y = \sqrt{1 + x^{2}}$
68304	Find the Derivative - d/dθ	y=sin(theta)cos(theta)	$y = \sin (θ) \cos (θ)$
68305	Find the Derivative - d/dθ	y=csc(theta)(theta+cot(theta))	$y = \csc (θ) (θ + \cot (θ))$
68306	Find the Maximum/Minimum Value	f(x)=4-2sin(2x-pi/4)	$f (x) = 4 - 2 \sin (2 x - \frac{π}{4})$
68307	Find dy/dx	2y^2=(5x-3)/(5x+3)	$2 y^{2} = \frac{5 x - 3}{5 x + 3}$
68308	Find dy/dx	y=e^(5 square root of x)	$y = e^{5 \sqrt{x}}$
68309	Evaluate the Limit	limit as x approaches infinity of (1+1/x)^(2x)	$lim_{x \to \infty} {(1 + \frac{1}{x})}^{2 x}$
68310	Use Logarithmic Differentiation to Find the Derivative	y=x^(6cos(x))	$y = x^{6 \cos (x)}$
68311	Maximize the Equation given the Constraints	F=5x+2y x+2y<=6 , x>=0 and y>=0 2x+y<=6	$F = 5 x + 2 y$ $x + 2 y \leq 6$ , $x \geq 0$ and $y \geq 0$ $2 x + y \leq 6$
68312	Integrate By Parts	integral of xe^(6x) with respect to x	$\int x e^{6 x} d x$
68313	Evaluate the Limit	limit as x approaches infinity of ( square root of x^2-9)/(2x-6)	$lim_{x \to \infty} \frac{\sqrt{x^{2} - 9}}{2 x - 6}$
68314	Find dy/dx	y=x^(3/2)	$y = x^{\frac{3}{2}}$
68315	Find the Derivative - d/dx	6sin(x)-8e^x	$6 \sin (x) - 8 e^{x}$
68316	Find the Derivative - d/dx	(1+x^2)^2	${(1 + x^{2})}^{2}$
68317	Find the Antiderivative	x*e^x	$x \cdot e^{x}$
68318	Evaluate the Limit	limit as x approaches pi/2 of (sin(x)-1)/(cos(x)^2)	$lim_{x \to \frac{π}{2}} \frac{\sin (x) - 1}{\cos^{2} (x)}$
68319	Evaluate the Integral	integral from -1 to 2 of (2x+3) with respect to x	$\int_{- 1}^{2} (2 x + 3) d x$
68320	Find the Antiderivative	x^2+x	$x^{2} + x$
68321	Find the Tangent Line at (1,2)	y=3x^2-x^3 , (1,2)	$y = 3 x^{2} - x^{3}$ , $(1, 2)$
68322	Evaluate the Integral	integral from 0 to pi of 9sin(t)^2cos(t)^4 with respect to t	$\int_{0}^{π} 9 \sin^{2} (t) \cos^{4} (t) d t$
68323	Find dy/dx	y+x/2=y^2	$y + \frac{x}{2} = y^{2}$
68324	Find the Derivative - d/dx	x^2-2y	$x^{2} - 2 y$
68325	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of tan(6x)^x	$lim_{x \to 0^{+}} {\tan (6 x)}^{x}$
68326	Find dy/dx	2y^2=(3x-5)/(3x+5)	$2 y^{2} = \frac{3 x - 5}{3 x + 5}$
68327	Evaluate the Limit	limit as h approaches -5 of (h^2-5^2)/(2h^2+11h+5)	$lim_{h \to - 5} \frac{h^{2} - 5^{2}}{2 h^{2} + 11 h + 5}$
68328	Find the Relative Extrema	f(x)=x^3-3x^2+1	$f (x) = x^{3} - 3 x^{2} + 1$
68329	Find the Derivative - d/dx	y=4x^2-1/x	$y = 4 x^{2} - \frac{1}{x}$
68330	Find the Derivative - d/dx	d/(dx)(-2/(x^4)+1/(x^3)-x)	$\frac{d}{d x} (\frac{- 2}{x^{4}} + \frac{1}{x^{3}} - x)$
68331	Find the Derivative - d/dx	(1+x^2)/x	$\frac{1 + x^{2}}{x}$
68332	Integrate By Parts	integral of x square root of x+2 with respect to x	$\int x \sqrt{x + 2} d x$
68333	Find da/dt	a^4-t^4=6a^2t	$a^{4} - t^{4} = 6 a^{2} t$
68334	Use Logarithmic Differentiation to Find the Derivative	y=sin(x)^(cos(x))	$y = {\sin (x)}^{\cos (x)}$
68335	Find dy/dx	y=(sin(x))/(1+cos(x))	$y = \frac{\sin (x)}{1 + \cos (x)}$
68336	Evaluate the Limit	limit as x approaches -5 of 1/(x+5)+11/((x+5)(x-6))	$lim_{x \to - 5} \frac{1}{x + 5} + \frac{11}{(x + 5) (x - 6)}$
68337	Find dy/dx	xsin(y)+ysin(x)=7	$x \sin (y) + y \sin (x) = 7$
68338	Find the Derivative - d/dx	d/(dx)( natural log of (5x+1)/(5x-1))	$\frac{d}{d x} (\ln (\frac{5 x + 1}{5 x - 1}))$
68339	Integrate Using Partial Fractions	integral of (x^3-x+3)/(x^2+x-2) with respect to x	$\int \frac{x^{3} - x + 3}{x^{2} + x - 2} d x$
68340	Find the Tangent Line at (1,0)	f(x)=(x^2-1)/(x^2+x+1) , (1,0)	$f (x) = \frac{x^{2} - 1}{x^{2} + x + 1}$ , $(1, 0)$
68341	Evaluate the Integral	integral of (4x^3-2sec(x)^2) with respect to x	$\int (4 x^{3} - 2 \sec^{2} (x)) d x$
68342	Find dy/dx	y = square root of 9-x^2	$y = \sqrt{9 - x^{2}}$
68343	Find dy/dx	y=e^(sin(x))	$y = e^{\sin (x)}$
68344	Evaluate the Limit	limit as x approaches 4 of f(x)=(x^2-2x-8)/(x-4)	$lim_{x \to 4} f (x) = \frac{x^{2} - 2 x - 8}{x - 4}$
68345	Find the Derivative - d/dx	y=5/((2x)^3)	$y = \frac{5}{{(2 x)}^{3}}$
68346	Evaluate the Limit	limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h	$lim_{h \to 0} \frac{\sin (\frac{π}{3} + h) - \sin (\frac{π}{3})}{h}$
68347	Find the Second Derivative	x natural log of x	$x \ln (x)$
68348	Evaluate the Integral	integral from -1 to 1 of e^x with respect to x	$\int_{- 1}^{1} e^{x} d x$
68349	Find the Maximum/Minimum Value	y=2x^2	$y = 2 x^{2}$
68350	Evaluate the Integral	integral from negative infinity to 0 of 1/(3-4x) with respect to x	$\int_{- \infty}^{0} \frac{1}{3 - 4 x} d x$
68351	Find the Derivative - d/dx	d/(dx)((3x^2-1)/(x-2))	$\frac{d}{d x} (\frac{3 x^{2} - 1}{x - 2})$
68352	Maximize the Equation given the Constraints	F=4x+3y x+3y<=6 , x>=0 and y>=0 x+y<=4	$F = 4 x + 3 y$ $x + 3 y \leq 6$ , $x \geq 0$ and $y \geq 0$ $x + y \leq 4$
68353	Find Where Increasing/Decreasing	y=-x^3	$y = - x^{3}$
68354	Evaluate the Limit	limit as x approaches -1 of (x^2+x)/(x^2-x-2)	$lim_{x \to - 1} \frac{x^{2} + x}{x^{2} - x - 2}$
68355	Find dy/dx	y=e^(-4x)	$y = e^{- 4 x}$
68356	Find dr/dV	V=4/3pir^3	$V = \frac{4}{3} π r^{3}$
68357	Find the Derivative - d/dθ	3tan(theta)	$3 \tan (θ)$
68358	Evaluate the Limit	limit as x approaches infinity of (x^3-2x^2+3x-4)/(4x^3-3x^2+2x-1)	$lim_{x \to \infty} \frac{x^{3} - 2 x^{2} + 3 x - 4}{4 x^{3} - 3 x^{2} + 2 x - 1}$
68359	Find dy/dx	x^3+y^3=8xy-5	$x^{3} + y^{3} = 8 x y - 5$
68360	Find dy/dx	1+x=sin(xy^2)	$1 + x = \sin (x y^{2})$
68361	Integrate By Parts	integral of xe^(x^2) with respect to x	$\int x e^{x^{2}} d x$
68362	Find the Derivative - d/dx	3f(x)	$3 f (x)$
68363	Evaluate the Integral	integral from 1 to 9 of (2+x^2)/( square root of x) with respect to x	$\int_{1}^{9} \frac{2 + x^{2}}{\sqrt{x}} d x$
68364	Solve the Differential Equation	(dy)/(dx)=3x^2y^2	$\frac{d y}{d x} = 3 x^{2} y^{2}$
68365	Find the Derivative - d/dx	d/(dx)( fourth root of x)	$\frac{d}{d x} (\sqrt[4]{x})$
68366	Find the Derivative - d/dx	y=3x^(5/4)	$y = 3 x^{\frac{5}{4}}$
68367	Find the Derivative - d/dx	1/(x^4)-3/(x^2)+x^3	$\frac{1}{x^{4}} - \frac{3}{x^{2}} + x^{3}$
68368	Integrate By Parts	integral of arcsin(x) with respect to x	$\int \arcsin (x) d x$
68369	Find the Derivative - d/dx	f( square root of x)	$f (\sqrt{x})$
68370	Integrate Using u-Substitution	integral of (x+2)/((x^2+4x)^2) with respect to x	$\int \frac{x + 2}{{(x^{2} + 4 x)}^{2}} d x$
68371	Find the Derivative - d/dx	3 square root of sin(x)	$3 \sqrt{\sin (x)}$
68372	Find the Derivative - d/dX	X^(1/6)	$X^{\frac{1}{6}}$
68373	Find the Derivative - d/dx	1/2xy	$\frac{1}{2} x y$
68374	Find dy/dx	(dy)/(dx)=x/y	$\frac{d y}{d x} = \frac{x}{y}$
68375	Integrate Using Trig Substitution	integral of (x^2)/( square root of 25-x^2) with respect to x	$\int \frac{x^{2}}{\sqrt{25 - x^{2}}} d x$
68376	Find dx/dy	x^2+xy+y^3=0	$x^{2} + x y + y^{3} = 0$
68377	Find dy/dx	y=x^(1/2)	$y = x^{\frac{1}{2}}$
68378	Find the Derivative - d/dx	d/(dx)(e^xsin(x))	$\frac{d}{d x} (e^{x} \sin (x))$
68379	Find the Derivative - d/dx	(5-3x)/(x^2+3x)	$\frac{5 - 3 x}{x^{2} + 3 x}$
68380	Evaluate the Integral	integral of x^4(5-x^2) with respect to x	$\int x^{4} (5 - x^{2}) d x$
68381	Find the Derivative - d/dx	y=x^9+cot(x)	$y = x^{9} + \cot (x)$
68382	Find dy/dx	3(x^2+y^2)^2=100xy	$3 {(x^{2} + y^{2})}^{2} = 100 x y$
68383	Find the Antiderivative	xcos(x)	$x \cos (x)$
68384	Evaluate the Integral	integral from 0 to a of 1/((1+x)^2) with respect to x=1/5	$\int_{0}^{a} \frac{1}{{(1 + x)}^{2}} d x = \frac{1}{5}$
68385	Evaluate the Integral	integral of (sin(2x))/(sin(x)) with respect to x	$\int \frac{\sin (2 x)}{\sin (x)} d x$
68386	Evaluate the Limit	limit as x approaches infinity of (6x^3)/(3x+2)	$lim_{x \to \infty} \frac{6 x^{3}}{3 x + 2}$
68387	Evaluate the Summation	sum from x=3 to 5 of -2/(x-2)	$\sum_{x = 3}^{5} \frac{- 2}{x - 2}$
68388	Find the Antiderivative	f(x)=7x^3-11x^2-2x+8	$f (x) = 7 x^{3} - 11 x^{2} - 2 x + 8$
68389	Find the Center and Radius	(x^2)/16+(y^2)/4=1	$\frac{x^{2}}{16} + \frac{y^{2}}{4} = 1$
68390	Evaluate the Limit	limit as x approaches negative infinity of (-2x^3+x^2+4x-4)/(-2x^3-2x^2-7x-7)	$lim_{x \to - \infty} \frac{- 2 x^{3} + x^{2} + 4 x - 4}{- 2 x^{3} - 2 x^{2} - 7 x - 7}$
68391	Find the Derivative - d/dx	(x^2+6x)/(10-x^2)	$\frac{x^{2} + 6 x}{10 - x^{2}}$
68392	Find the Derivative - d/dx	-(2x+y)/(x+2y)	$- \frac{2 x + y}{x + 2 y}$
68393	Find dy/dx	y=(x^-2+x)^-3	$y = {(x^{- 2} + x)}^{- 3}$
68394	Find dy/dx	y^2-x^3=9	$y^{2} - x^{3} = 9$
68395	Find the Derivative - d/dx	-1/(2x^(3/2))	$- \frac{1}{2 x^{\frac{3}{2}}}$
68396	Find dy/dx	y=x^-12	$y = x^{- 12}$
68397	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (2-x)^(tan((pix)/2))	$lim_{x \to 1} {(2 - x)}^{\tan (\frac{π x}{2})}$
68398	Find dy/dx	x^2(x-y)^2=x^2-y^2	$x^{2} {(x - y)}^{2} = x^{2} - y^{2}$
68399	Find dy/dx	6 square root of y=x-y	$6 \sqrt{y} = x - y$
68400	Use Logarithmic Differentiation to Find the Derivative	y=x^(8cos(x))	$y = x^{8 \cos (x)}$