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Popular Calculus Problems

derivative of cos(3x+1)	\frac{d}{dx}(\cos(3x+1))
derivative of xsqrt(3-x)	\frac{d}{dx}(x\sqrt{3-x})
(\partial)/(\partial x)(-3xe^{2xy})	\frac{\partial\:}{\partial\:x}(-3xe^{2xy})
(dy)/(dx)=x(8-y)	\frac{dy}{dx}=x(8-y)
derivative of (cos(x))^2	derivative\:(\cos(x))^{2}
(4+x)y^'=9y	(4+x)y^{\prime\:}=9y
integral of x/(\sqrt[3]{x-6)}	\int\:\frac{x}{\sqrt[3]{x-6}}dx
(\partial)/(\partial x)(y^2-4x)	\frac{\partial\:}{\partial\:x}(y^{2}-4x)
derivative of (x^3/(1+x^2))	\frac{d}{dx}(\frac{x^{3}}{1+x^{2}})
sum from n=0 to infinity of (n+1)/(2n-3)	\sum\:_{n=0}^{\infty\:}\frac{n+1}{2n-3}
integral of (2x-2)/(1+(x-1)^2)	\int\:\frac{2x-2}{1+(x-1)^{2}}dx
(dx)/(dt)=7(x^2+1),x(pi/4)=1	\frac{dx}{dt}=7(x^{2}+1),x(\frac{π}{4})=1
derivative of 6t^2-4t+9	derivative\:6t^{2}-4t+9
laplacetransform f(t)=2e^{-t}cos(4t)	laplacetransform\:f(t)=2e^{-t}\cos(4t)
integral of (cos(2x))/((1+sin(2x))^2)	\int\:\frac{\cos(2x)}{(1+\sin(2x))^{2}}dx
derivative of sqrt(12x-x^2)	\frac{d}{dx}(\sqrt{12x-x^{2}})
integral of 6sin^5(x)cos(x)	\int\:6\sin^{5}(x)\cos(x)dx
derivative of 3/4 x^{4/3}-3/8 x^{2/3}+8	\frac{d}{dx}(\frac{3}{4}x^{\frac{4}{3}}-\frac{3}{8}x^{\frac{2}{3}}+8)
derivative of x^4-3x^2+4	\frac{d}{dx}(x^{4}-3x^{2}+4)
integral of x(x-1)(x-2)	\int\:x(x-1)(x-2)dx
derivative of y=(2x^2-3)^2	derivative\:y=(2x^{2}-3)^{2}
integral from 1 to 9 of 4sqrt(x)	\int\:_{1}^{9}4\sqrt{x}dx
integral of-2picos^4(pix)sin^5(pix)	\int\:-2π\cos^{4}(πx)\sin^{5}(πx)dx
integral of 5xsqrt(2x+3)	\int\:5x\sqrt{2x+3}dx
integral of 1/(sqrt(x)(1+\sqrt{x))^3}	\int\:\frac{1}{\sqrt{x}(1+\sqrt{x})^{3}}dx
limit as x approaches 2 of ax^2-2bx+1	\lim\:_{x\to\:2}(ax^{2}-2bx+1)
y^'-9/x y=((y^5))/(x^8)	y^{\prime\:}-\frac{9}{x}y=\frac{(y^{5})}{x^{8}}
derivative of y=sin(5x)	derivative\:y=\sin(5x)
integral of 1/(2t)	\int\:\frac{1}{2t}dt
tangent of f(x)=x^3,\at x=2	tangent\:f(x)=x^{3},\at\:x=2
integral of 4xarctan(x)	\int\:4x\arctan(x)dx
limit as x approaches 9 of 1/(x-9)	\lim\:_{x\to\:9}(\frac{1}{x-9})
derivative of (x+2/x (7-2x^3))	\frac{d}{dx}((x+\frac{2}{x})(7-2x^{3}))
1/y (dy)/(dx)=e^x+ln(y)	\frac{1}{y}\frac{dy}{dx}=e^{x}+\ln(y)
(8-r^2)dr=r^3sin(θ)dθ,r(0)=2	(8-r^{2})dr=r^{3}\sin(θ)dθ,r(0)=2
integral of 4x^3-6x^2+3	\int\:4x^{3}-6x^{2}+3dx
integral of 19tan^5(x)sec^4(x)	\int\:19\tan^{5}(x)\sec^{4}(x)dx
integral of 4x-2x^2	\int\:4x-2x^{2}dx
f(z)=sqrt((z-8)/(z+8))	f(z)=\sqrt{\frac{z-8}{z+8}}
limit as x approaches 3 of 5/(x^2-9)	\lim\:_{x\to\:3}(\frac{5}{x^{2}-9})
integral of e^{4θ}sin(5θ)	\int\:e^{4θ}\sin(5θ)dθ
limit as x approaches 48 of (x^2)/8-6/x	\lim\:_{x\to\:48}(\frac{x^{2}}{8}-\frac{6}{x})
derivative of (6t)/(6+sqrt(t))	derivative\:\frac{6t}{6+\sqrt{t}}
derivative of ((x+2)(x^2-2x+4))/(x^3)	derivative\:\frac{(x+2)(x^{2}-2x+4)}{x^{3}}
integral of 250(e^{-0.2x}-1)	\int\:250(e^{-0.2x}-1)dx
derivative of x/((x^2+y^2))	\frac{d}{dx}(\frac{x}{(x^{2}+y^{2})})
derivative of (x+2)^{1/2}	derivative\:(x+2)^{\frac{1}{2}}
(x^2+49)(dy)/(dx)=7	(x^{2}+49)\frac{dy}{dx}=7
taylor 4x^4+3x^3+2x^2+x+1,1	taylor\:4x^{4}+3x^{3}+2x^{2}+x+1,1
(\partial)/(\partial x)(-5ye^x)	\frac{\partial\:}{\partial\:x}(-5ye^{x})
derivative of 12^x	\frac{d}{dx}(12^{x})
derivative of x^2-4x+5	\frac{d}{dx}(x^{2}-4x+5)
derivative of pi/4	\frac{d}{dx}(\frac{π}{4})
integral of 1/(x-10)	\int\:\frac{1}{x-10}dx
integral of 2/(2x-1)	\int\:\frac{2}{2x-1}dx
derivative of-(14)/(s^6)	derivative\:-\frac{14}{s^{6}}
integral of 0.5sin(2x)	\int\:0.5\sin(2x)dx
integral of sqrt(9x^4+4x^2)	\int\:\sqrt{9x^{4}+4x^{2}}dx
(\partial)/(\partial x)(2sqrt(x^2+2y^2))	\frac{\partial\:}{\partial\:x}(2\sqrt{x^{2}+2y^{2}})
(dy)/(dx)=(y^2-1)/(x^2-1),y(9)=9	\frac{dy}{dx}=\frac{y^{2}-1}{x^{2}-1},y(9)=9
d/(dy)((1/(y^2)-3/(y^4))(y+9y^3))	\frac{d}{dy}((\frac{1}{y^{2}}-\frac{3}{y^{4}})(y+9y^{3}))
derivative of 2csc(1-3x)	derivative\:2\csc(1-3x)
tangent of f(x)=(2x+3)^5,\at x=-1	tangent\:f(x)=(2x+3)^{5},\at\:x=-1
derivative of \sqrt[4]{x}-4/x	\frac{d}{dx}(\sqrt[4]{x}-\frac{4}{x})
(dy)/(dx)-2y=0	\frac{dy}{dx}-2y=0
integral of sin^3(xco)s^7x	\int\:\sin^{3}(xco)s^{7}xdx
(cos(6x))y^'+6(tan(6x))y=-sec(6x)	(\cos(6x))y^{\prime\:}+6(\tan(6x))y=-\sec(6x)
(\partial)/(\partial x)((2x)/((x-y)^2))	\frac{\partial\:}{\partial\:x}(\frac{2x}{(x-y)^{2}})
integral of sqrt(4x^2+x^4)	\int\:\sqrt{4x^{2}+x^{4}}dx
tdt+ye^{-t}dy=0	tdt+ye^{-t}dy=0
derivative of 5x+2	\frac{d}{dx}(5x+2)
(\partial)/(\partial x)(sin(xye^{x^2}))	\frac{\partial\:}{\partial\:x}(\sin(x\cdot\:y\cdot\:e^{x^{2}}))
f^'(x)=2^{4x}+4x^2	f^{\prime\:}(x)=2^{4x}+4x^{2}
integral of (1-2x)^9	\int\:(1-2x)^{9}dx
derivative of e^t*cos(2t)	derivative\:e^{t}\cdot\:\cos(2t)
integral of ((2x)/(1+x^2))	\int\:(\frac{2x}{1+x^{2}})dx
integral of ((x+1))/(x^2(x-1))	\int\:\frac{(x+1)}{x^{2}(x-1)}dx
x(dy)/(dx)+y=y^{-2}	x\frac{dy}{dx}+y=y^{-2}
integral from-infinity to 0 of xe^{(3x)}	\int\:_{-\infty\:}^{0}xe^{(3x)}dx
derivative of 4sin^2(x+9cos^3(x))	\frac{d}{dx}(4\sin^{2}(x)+9\cos^{3}(x))
integral of (x^3)/(x^2-25)	\int\:\frac{x^{3}}{x^{2}-25}dx
(\partial)/(\partial x)(sqrt(x^2-2x+3))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}-2x+3})
derivative of (4x/3)	\frac{d}{dx}(\frac{4x}{3})
area 8/(1+x^4),4x^2	area\:\frac{8}{1+x^{4}},4x^{2}
y^'+y/t =3cos(2t)	y^{\prime\:}+\frac{y}{t}=3\cos(2t)
(dy)/(dx)=(y+x)/(y-x)	\frac{dy}{dx}=\frac{y+x}{y-x}
(dx)/(dt)=5x	\frac{dx}{dt}=5x
derivative of bsin(x)	\frac{d}{dx}(b\sin(x))
limit as x approaches 4 of-2x^2	\lim\:_{x\to\:4}(-2x^{2})
limit as x approaches-infinity of-2x^5	\lim\:_{x\to\:-\infty\:}(-2x^{5})
tangent of f(x)=x^3-9x^2+10x,\at x=1	tangent\:f(x)=x^{3}-9x^{2}+10x,\at\:x=1
tangent of x^2-5x,\at x=4	tangent\:x^{2}-5x,\at\:x=4
derivative of arctan(x^3)	\frac{d}{dx}(\arctan(x^{3}))
derivative of e^{-st}dt	derivative\:e^{-st}dt
derivative of (x^2-2x+2/(x-1))	\frac{d}{dx}(\frac{x^{2}-2x+2}{x-1})
integral of sqrt(1+4y^2)	\int\:\sqrt{1+4y^{2}}dy
derivative of (ln(x))/(x^3)	derivative\:\frac{\ln(x)}{x^{3}}
(\partial)/(\partial x)(cos(x/2))	\frac{\partial\:}{\partial\:x}(\cos(\frac{x}{2}))
derivative of f(x)=(x^{12})/(x^2)	derivative\:f(x)=\frac{x^{12}}{x^{2}}
derivative of (8x)/(x^2+1)	derivative\:\frac{8x}{x^{2}+1}

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