Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69401	Find dy/dx	xe^y=2xy+y^3	$x e^{y} = 2 x y + y^{3}$
69402	Find the Maximum/Minimum Value	y=x	$y = x$
69403	Find the Center and Radius	((y-3)^2)/49-((x+2)^2)/16=1	$\frac{{(y - 3)}^{2}}{49} - \frac{{(x + 2)}^{2}}{16} = 1$
69404	Find Where Increasing/Decreasing	f(x)=(x^2+1)/(x^2-1)	$f (x) = \frac{x^{2} + 1}{x^{2} - 1}$
69405	Evaluate the Integral	integral from 0 to pi/2 of sin(x)^2 with respect to x	$\int_{0}^{\frac{π}{2}} \sin^{2} (x) d x$
69406	Find the Derivative - d/dt	(t-1)^2	${(t - 1)}^{2}$
69407	Evaluate the Limit	limit as x approaches pi/4 of (cos(x)-sin(x))/(1-2sin(x)^2)	$lim_{x \to \frac{π}{4}} \frac{\cos (x) - \sin (x)}{1 - 2 \sin^{2} (x)}$
69408	Evaluate the Limit	limit as x approaches c of (f(x))/(g(x))	$lim_{x \to c} \frac{f (x)}{g (x)}$
69409	Evaluate the Limit	limit as x approaches 1/2 of 2e^(x^4+2/9)	$lim_{x \to \frac{1}{2}} 2 e^{x^{4} + \frac{2}{9}}$
69410	Evaluate the Integral	integral of (( square root of x-b)^2)/( square root of x) with respect to x	$\int \frac{{(\sqrt{x} - b)}^{2}}{\sqrt{x}} d x$
69411	Find the Derivative - d/dx	(2-x)/(3x+1)	$\frac{2 - x}{3 x + 1}$
69412	Evaluate the Limit	limit as x approaches infinity of (8x^2-3)/(7x^2+x-3)	$lim_{x \to \infty} \frac{8 x^{2} - 3}{7 x^{2} + x - 3}$
69413	Find the Integral	x*e^x	$x \cdot e^{x}$
69414	Find dx/dy	y=2x	$y = 2 x$
69415	Find the Derivative - d/dx	d/(dx)(-4x^(4/3)-2x^(-3/4)+3)	$\frac{d}{d x} (- 4 x^{\frac{4}{3}} - 2 x^{- \frac{3}{4}} + 3)$
69416	Find dy/dx	y=x^2e^(-x)	$y = x^{2} e^{- x}$
69417	Find dy/dx	cos(x+y)+y=x	$\cos (x + y) + y = x$
69418	Find the Second Derivative	square root of 1-y^2	$\sqrt{1 - y^{2}}$
69419	Solve the Differential Equation	(dy)/(dx)+2xy=0	$\frac{d y}{d x} + 2 x y = 0$
69420	Evaluate the Limit	limit as x approaches pi/4 of (cos(x)-sin(x))/(tan(x)-1)	$lim_{x \to \frac{π}{4}} \frac{\cos (x) - \sin (x)}{\tan (x) - 1}$
69421	Find the Average Value of the Derivative	f(x)=x^2+2x-3 , [0,6]	$f (x) = x^{2} + 2 x - 3$ , $[0, 6]$
69422	Evaluate the Limit	limit as x approaches infinity of x/( natural log of x)	$lim_{x \to \infty} \frac{x}{\ln (x)}$
69423	Find the Derivative - d/dx	90+45cos((x^2)/18)	$90 + 45 \cos (\frac{x^{2}}{18})$
69424	Evaluate the Limit	limit as x approaches negative infinity of ((x-3)(x+2))/(2x^2+x+1)	$lim_{x \to - \infty} \frac{(x - 3) (x + 2)}{2 x^{2} + x + 1}$
69425	Find the Derivative - d/dx	y=x^2 square root of 1-x^2	$y = x^{2} \sqrt{1 - x^{2}}$
69426	Find the Derivative - d/dx	x+y^2	$x + y^{2}$
69427	Find the Derivative - d/dx	x^2+ square root of x	$x^{2} + \sqrt{x}$
69428	Determine if Continuous	f(x)=x^2,x<3; 6x-9,x>=3	$f (x) = {\begin{cases} x^{2}, x < 3 \\ 6 x - 9, x \geq 3 \end{cases}$
69429	Find dx/dy	x^2y+y^2x=-2	$x^{2} y + y^{2} x = - 2$
69430	Find the Derivative - d/dx	(x^2+2x)/(4-5x)	$\frac{x^{2} + 2 x}{4 - 5 x}$
69431	Find the Derivative - d/dθ	cot(theta)^2	$\cot^{2} (θ)$
69432	Evaluate the Integral	integral from 0 to 1 of (3x-2 square root of x) with respect to x	$\int_{0}^{1} (3 x - 2 \sqrt{x}) d x$
69433	Find the Derivative - d/dx	(x^2)/( natural log of x)	$\frac{x^{2}}{\ln (x)}$
69434	Find the Tangent Line at (1,1)	y=(2x+1)/(x+2) , (1,1)	$y = \frac{2 x + 1}{x + 2}$ , $(1, 1)$
69435	Evaluate the Limit	limit as x approaches 4 of 2^x+ square root of x+5	$lim_{x \to 4} 2^{x} + \sqrt{x + 5}$
69436	Find dx/dy	y=(2x^-2+3)^-3	$y = {(2 x^{- 2} + 3)}^{- 3}$
69437	Find the Derivative - d/dx	y=(x^3-6x)(2-4x^3)	$y = (x^{3} - 6 x) (2 - 4 x^{3})$
69438	Find the Derivative of the Integral	F(x) = integral from square root of x to 2x of arctan(t) with respect to t	$F (x) = \int_{\sqrt{x}}^{2 x} \arctan (t) d t$
69439	Evaluate the Integral	integral of square root of t(t^2+3t+2) with respect to t	$\int \sqrt{t} (t^{2} + 3 t + 2) d t$
69440	Use Logarithmic Differentiation to Find the Derivative	y=x^(e^x)	$y = x^{e^{x}}$
69441	Find the Derivative - d/dx	square root of x+x	$\sqrt{x} + x$
69442	Find the Maximum/Minimum Value	f(x)=x^2e^x	$f (x) = x^{2} e^{x}$
69443	Evaluate the Integral	integral of (tan(y)^2+1) with respect to y	$\int (\tan^{2} (y) + 1) d y$
69444	Find the Antiderivative	a^x	$a^{x}$
69445	Find dy/dx	4x^2=2y^3+4y	$4 x^{2} = 2 y^{3} + 4 y$
69446	Find the Tangent Line at (0,9)	y=x^4+9e^x , (0,9)	$y = x^{4} + 9 e^{x}$ , $(0, 9)$
69447	Solve the Differential Equation	x(dy)/(dx)=4y-3 , y(1)=1	$x \frac{d y}{d x} = 4 y - 3$ , $y (1) = 1$
69448	Evaluate the Limit	limit as x approaches infinity of square root of x-x	$lim_{x \to \infty} \sqrt{x} - x$
69449	Find dy/dx	y=x^2sin(8x)	$y = x^{2} \sin (8 x)$
69450	Verify the Differential Equation Solution	y''''=y-2x , y=3x	$y'' = y - 2 x$ , $y = 3 x$
69451	Find Where Increasing/Decreasing	f(x)=3x^4-4x^3-12x^2+5	$f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$
69452	Find the Relative Extrema	y=x^3-12x+3	$y = x^{3} - 12 x + 3$
69453	Evaluate the Integral	integral of (x^4-1/2x^3+1/4x-2) with respect to x	$\int (x^{4} - \frac{1}{2} x^{3} + \frac{1}{4} x - 2) d x$
69454	Find the Derivative - d/dx	y=(4x+1)(1-x)^3	$y = (4 x + 1) {(1 - x)}^{3}$
69455	Find dy/dx	x^3y^4-6e^(2x-y)=3	$x^{3} y^{4} - 6 e^{2 x - y} = 3$
69456	Integrate By Parts	integral of arccos(x) with respect to x	$\int \arccos (x) d x$
69457	Find the Integral	1/((1-x)^2)	$\frac{1}{{(1 - x)}^{2}}$
69458	Find the Maximum/Minimum Value	f(x)=(x^2)/(x^2-16)	$f (x) = \frac{x^{2}}{x^{2} - 16}$
69459	Solve the Differential Equation	x^2(dy)/(dx)=y-xy	$x^{2} \frac{d y}{d x} = y - x y$
69460	Find dx/dy	y=sin(xy)	$y = \sin (x y)$
69461	Evaluate the Integral	integral from 1/( square root of 3) to square root of 3 of 3/(1+x^2) with respect to x	$\int_{\frac{1}{\sqrt{3}}}^{\sqrt{3}} \frac{3}{1 + x^{2}} d x$
69462	Find the Slope	f(x)=x^2	$f (x) = x^{2}$
69463	Find dy/dx	y=(x^2+1)^3	$y = {(x^{2} + 1)}^{3}$
69464	Find dx/dy	y=arcsin(2x+1)	$y = \arcsin (2 x + 1)$
69465	Find the Maximum/Minimum Value	f(x)=x^3+9x^2	$f (x) = x^{3} + 9 x^{2}$
69466	Find the Derivative - d/dx	f(-4)	$f (- 4)$
69467	Find the Derivative - d/dx	arcsin(x/2)	$\arcsin (\frac{x}{2})$
69468	Find the Derivative - d/dx	e^(2x)(x^3+1)	$e^{2 x} (x^{3} + 1)$
69469	Find dV/dh	V=pir^2h	$V = π r^{2} h$
69470	Find the Fourth Derivative	f(x)=xe^(-x)	$f (x) = x e^{- x}$
69471	Find the Derivative - d/dx	d/(dx)((-2x^4-x^-2-4)/(-4x^7))	$\frac{d}{d x} (\frac{- 2 x^{4} - x^{- 2} - 4}{- 4 x^{7}})$
69472	Integrate Using Trig Substitution	integral of 1/(x square root of 4x^2+9) with respect to x	$\int \frac{1}{x \sqrt{4 x^{2} + 9}} d x$
69473	Find dy/dx	square root of x+y=xy	$\sqrt{x + y} = x y$
69474	Evaluate the Summation	sum from i=4 to 10 of (i-i^2)/3	$\sum_{i = 4}^{10} \frac{i - i^{2}}{3}$
69475	Evaluate the Limit	limit as x approaches 0 of (5x+cos(-5x)-1)/(-2x)	$lim_{x \to 0} \frac{5 x + \cos (- 5 x) - 1}{- 2 x}$
69476	Find dy/dx	y = square root of 3x	$y = \sqrt{3 x}$
69477	Evaluate the Integral	integral from 1 to 3 of (2x^2-12x+13) with respect to x	$\int_{1}^{3} (2 x^{2} - 12 x + 13) d x$
69478	Find the Derivative - d/dx	y = square root of (2x)/(x+1)	$y = \sqrt{\frac{2 x}{x + 1}}$
69479	Find dy/dx	2 square root of y=x-5y	$2 \sqrt{y} = x - 5 y$
69480	Integrate Using Trig Substitution	integral of 1/(x^2 square root of x^2-9) with respect to x	$\int \frac{1}{x^{2} \sqrt{x^{2} - 9}} d x$
69481	Find Where Increasing/Decreasing	f(x)=(3/2)^x	$f (x) = {(\frac{3}{2})}^{x}$
69482	Find dy/dx	x^4+xy^3-y^2=4	$x^{4} + x y^{3} - y^{2} = 4$
69483	Integrate Using Trig Substitution	integral of x^3 square root of 1-x^2 with respect to x	$\int x^{3} \sqrt{1 - x^{2}} d x$
69484	Find the Maximum/Minimum Value	C(x)=x^(1/3)(x+4)	$C (x) = x^{\frac{1}{3}} (x + 4)$
69485	Find dy/dx	y^2=4ax	$y^{2} = 4 a x$
69486	Evaluate the Limit	limit as x approaches 0 of (2x^2+x)/(sin(x))	$lim_{x \to 0} \frac{2 x^{2} + x}{\sin (x)}$
69487	Evaluate the Limit	limit as x approaches 0 of (xtan(x))/(1-cos(2x))	$lim_{x \to 0} \frac{x \tan (x)}{1 - \cos (2 x)}$
69488	Find the Derivative - d/dx	y=sin(x^2)^2	$y = \sin^{2} (x^{2})$
69489	Evaluate the Limit	limit as x approaches 0 of 2^x-1/2	$lim_{x \to 0} 2^{x} - \frac{1}{2}$
69490	Find dx/dy	x^3y^3-y=x	$x^{3} y^{3} - y = x$
69491	Find the Arc Length	x=(y^4)/8+1/(4y^2) , 1<=y<=3	$x = \frac{y^{4}}{8} + \frac{1}{4 y^{2}}$ , $1 \leq y \leq 3$
69492	Solve the Differential Equation	(dy)/(dx)=(x^2)/(1-y^2)	$\frac{d y}{d x} = \frac{x^{2}}{1 - y^{2}}$
69493	Find the Tangent Line at (5,0)	y = natural log of x^2-5x+1 , (5,0)	$y = \ln (x^{2} - 5 x + 1)$ , $(5, 0)$
69494	Find the Derivative - d/dx	y=(2x+3) square root of x^2+3x	$y = (2 x + 3) \sqrt{x^{2} + 3 x}$
69495	Find dy/dx	y = square root of (x^2-1)/(x^2+1)	$y = \sqrt{\frac{x^{2} - 1}{x^{2} + 1}}$
69496	Solve the Differential Equation	x(dy)/(dx)-4y=x^6e^x	$x \frac{d y}{d x} - 4 y = x^{6} e^{x}$
69497	Find the Maximum/Minimum Value	g(x)=x^3-15x	$g (x) = x^{3} - 15 x$
69498	Find the Antiderivative	( square root of x)/x	$\frac{\sqrt{x}}{x}$
69499	Evaluate the Limit	limit as x approaches 2 of (x^3+x^2-4x-4)/(x^4-16)	$lim_{x \to 2} \frac{x^{3} + x^{2} - 4 x - 4}{x^{4} - 16}$
69500	Find the Derivative - d/dx	y=x/3(2x+1)^3	$y = \frac{x}{3} {(2 x + 1)}^{3}$