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Popular Calculus Problems

(\partial)/(\partial z)(xcos(y)sin(z))	\frac{\partial\:}{\partial\:z}(x\cdot\:\cos(y)\cdot\:\sin(z))
d/(dt)(1/(sqrt(t^2+1)))	\frac{d}{dt}(\frac{1}{\sqrt{t^{2}+1}})
(\partial)/(\partial x)((x+y^2)*e^{3x-2y})	\frac{\partial\:}{\partial\:x}((x+y^{2})\cdot\:e^{3x-2y})
(6xdy)/(dx)=2xe^x-6y+6x^2	\frac{6xdy}{dx}=2xe^{x}-6y+6x^{2}
derivative of 30ln(5x+1)	\frac{d}{dx}(30\ln(5x+1))
inverse oflaplace {4/s+6/(s^5)-1/(s+8)}	inverselaplace\:\left\{\frac{4}{s}+\frac{6}{s^{5}}-\frac{1}{s+8}\right\}
integral of e^{2z}	\int\:e^{2z}dz
derivative of arctan(xsqrt(t))	\frac{d}{dx}(\arctan(x\sqrt{t}))
(\partial)/(\partial x)((3x)/(sqrt(x^2+2)))	\frac{\partial\:}{\partial\:x}(\frac{3x}{\sqrt{x^{2}+2}})
integral of (11)/(sqrt(1-x^2))	\int\:\frac{11}{\sqrt{1-x^{2}}}dx
derivative of 8x^2sin(xtan(x))	\frac{d}{dx}(8x^{2}\sin(x)\tan(x))
(dy}{dx}=\frac{y^2-y)/x	\frac{dy}{dx}=\frac{y^{2}-y}{x}
x^2y^{''}-4xy^'+6y=0,y(1)=0.4,y^'(1)=0	x^{2}y^{\prime\:\prime\:}-4xy^{\prime\:}+6y=0,y(1)=0.4,y^{\prime\:}(1)=0
ydx-(x+y)dy=0	ydx-(x+y)dy=0
slope of (5,-5),(-3,5)	slope\:(5,-5),(-3,5)
y^{'''}-7y^{''}+8y^'+16y=0	y^{\prime\:\prime\:\prime\:}-7y^{\prime\:\prime\:}+8y^{\prime\:}+16y=0
derivative of In(sin(x))	\frac{d}{dx}(In(\sin(x)))
integral of x^2xsin(x^2)	\int\:x^{2}x\sin(x^{2})dx
derivative of arctan(x^2)	derivative\:\arctan(x^{2})
d/(dz)(2z)	\frac{d}{dz}(2z)
derivative of f(x)=sin(x^2)+(1-x)/(1+x)	derivative\:f(x)=\sin(x^{2})+\frac{1-x}{1+x}
integral from 6 to 7 of xsqrt(x-6)	\int\:_{6}^{7}x\sqrt{x-6}dx
derivative of 3x^2-12	\frac{d}{dx}(3x^{2}-12)
integral of 1/(8x^7)	\int\:\frac{1}{8x^{7}}dx
(dy)/(dt)=0.28-((7y))/(1000)	\frac{dy}{dt}=0.28-\frac{(7y)}{1000}
derivative of (x^3/(x^4+1))	\frac{d}{dx}(\frac{x^{3}}{x^{4}+1})
integral of ((2-x)^3)/3	\int\:\frac{(2-x)^{3}}{3}dx
derivative of sin(x+5/2)	derivative\:\sin(x+\frac{5}{2})
(dy)/(dx)= 4/(x^2-1)	\frac{dy}{dx}=\frac{4}{x^{2}-1}
limit as x approaches 1+of (1+x)/(1-x)	\lim\:_{x\to\:1+}(\frac{1+x}{1-x})
derivative of 6e	\frac{d}{dx}(6e)
integral of (-4x-10)/(x^3)	\int\:\frac{-4x-10}{x^{3}}dx
area f(x)=x^2-12,g(x)=x-6,x=-2,x=3	area\:f(x)=x^{2}-12,g(x)=x-6,x=-2,x=3
integral of 3x^7+4x^5-2x^3-x+1	\int\:3x^{7}+4x^{5}-2x^{3}-x+1dx
derivative of ((2x-1^3)/((x-3)^2))	\frac{d}{dx}(\frac{(2x-1)^{3}}{(x-3)^{2}})
(\partial)/(\partial x)(ze^{xy})	\frac{\partial\:}{\partial\:x}(ze^{xy})
derivative of (1400/((1+6e^{-0.02x))})	\frac{d}{dx}(\frac{1400}{(1+6e^{-0.02x})})
taylor f(x)=x^{-2}	taylor\:f(x)=x^{-2}
derivative of (sin(x)/(xy))	\frac{d}{dx}(\frac{\sin(x)}{xy})
integral of 2x^2+3x-1	\int\:2x^{2}+3x-1dx
derivative of f(x)= x/(x^2+5)	derivative\:f(x)=\frac{x}{x^{2}+5}
integral from 0 to 3 of x^2e^{-x}	\int\:_{0}^{3}x^{2}e^{-x}dx
derivative of x^{5/2}	derivative\:x^{\frac{5}{2}}
integral of (log_{e}(x))^2	\int\:(\log_{e}(x))^{2}dx
integral of (sqrt(x^2+4))/x	\int\:\frac{\sqrt{x^{2}+4}}{x}dx
integral of (4/(x^2)+2-1/(8x^3))	\int\:(\frac{4}{x^{2}}+2-\frac{1}{8x^{3}})dx
integral from 0 to 1 of \sqrt[3]{x}-x^3	\int\:_{0}^{1}\sqrt[3]{x}-x^{3}dx
integral from 0 to 1 of sin(pit)	\int\:_{0}^{1}\sin(πt)dt
derivative of x/(sqrt(x^2+y^2))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+y^{2}}})
integral of sqrt(1-cos^2(x))	\int\:\sqrt{1-\cos^{2}(x)}dx
derivative of-4x^3+4x	\frac{d}{dx}(-4x^{3}+4x)
area x^2,(0,3)	area\:x^{2},(0,3)
integral of c(x)	\int\:c(x)dx
derivative of h(x)=[(x+1)/(x-1)]^3	derivative\:h(x)=[\frac{x+1}{x-1}]^{3}
(\partial)/(\partial x)((y/z)^{1/x})	\frac{\partial\:}{\partial\:x}((\frac{y}{z})^{\frac{1}{x}})
y^{''}+3y=48x^2e^{3x}	y^{\prime\:\prime\:}+3y=48x^{2}e^{3x}
limit as x approaches 1 of x^{1/(1-x^2)}	\lim\:_{x\to\:1}(x^{\frac{1}{1-x^{2}}})
derivative of f(x)=x^{-4}	derivative\:f(x)=x^{-4}
inverse oflaplace (s^2+1)/(s^2+2s+2)	inverselaplace\:\frac{s^{2}+1}{s^{2}+2s+2}
integral of ((e^x))/x	\int\:\frac{(e^{x})}{x}dx
tangent of f(x)2x^2+8x,x=1	tangent\:f(x)2x^{2}+8x,x=1
limit as x approaches 0 of (tan(6x))^x	\lim\:_{x\to\:0}((\tan(6x))^{x})
(\partial)/(\partial x)(x+y+x^3+y^2)	\frac{\partial\:}{\partial\:x}(x+y+x^{3}+y^{2})
y^'=x^2(x-2)^2(x-1)^2	y^{\prime\:}=x^{2}(x-2)^{2}(x-1)^{2}
integral from-1 to 1 of (3x^3-x^2+x-1)	\int\:_{-1}^{1}(3x^{3}-x^{2}+x-1)dx
derivative of x^3sin(7x)	derivative\:x^{3}\sin(7x)
(\partial)/(\partial x)(sin(7x+y+3z))	\frac{\partial\:}{\partial\:x}(\sin(7x+y+3z))
derivative of sqrt(6+7x)	\frac{d}{dx}(\sqrt{6+7x})
taylor e^{3x},0	taylor\:e^{3x},0
inverse oflaplace (2s-3)/(s^2+2)	inverselaplace\:\frac{2s-3}{s^{2}+2}
integral of (7x)/(x^2+1)	\int\:\frac{7x}{x^{2}+1}dx
derivative of f(x)=sec(θ)tan(θ)	derivative\:f(x)=\sec(θ)\tan(θ)
integral of x^2(5x^2+x)^2	\int\:x^{2}(5x^{2}+x)^{2}dx
(\partial)/(\partial h)(1/2 (a+b)h)	\frac{\partial\:}{\partial\:h}(\frac{1}{2}(a+b)h)
derivative of 2/(x^{1/3}-2)	\frac{d}{dx}(\frac{2}{x^{\frac{1}{3}}}-2)
derivative of f(x)=-5x(2x-3)^4	derivative\:f(x)=-5x(2x-3)^{4}
y^{''}-2y^'+5y=5,y(0)=2,y^'(0)=1	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=5,y(0)=2,y^{\prime\:}(0)=1
integral of ((1-tan^2(x)))/(sec^2(x))	\int\:\frac{(1-\tan^{2}(x))}{\sec^{2}(x)}dx
tangent of f(x)=((x-3)/(x+1))^2,\at x=0	tangent\:f(x)=(\frac{x-3}{x+1})^{2},\at\:x=0
integral of ye^{3y}	\int\:ye^{3y}dy
sum from n=0 to infinity of 1/(3+2n)	\sum\:_{n=0}^{\infty\:}\frac{1}{3+2n}
integral of (sin(x))/3	\int\:\frac{\sin(x)}{3}dx
integral from 1 to 2 of (x^2-4)	\int\:_{1}^{2}(x^{2}-4)dx
integral of 2cos^2(t)sin^2(t)	\int\:2\cos^{2}(t)\sin^{2}(t)dt
tangent of f(x)=x^2+3x+5,(1,9)	tangent\:f(x)=x^{2}+3x+5,(1,9)
integral of arccot(10x)	\int\:\arccot(10x)dx
(\partial)/(\partial y)(e^{(x+y)})	\frac{\partial\:}{\partial\:y}(e^{(x+y)})
integral of x/(sqrt(2x+7))	\int\:\frac{x}{\sqrt{2x+7}}dx
(\partial)/(\partial x)(5cos(7x-3y))	\frac{\partial\:}{\partial\:x}(5\cos(7x-3y))
limit as x approaches 2+of 1/(\|2-x\|)	\lim\:_{x\to\:2+}(\frac{1}{\left\|2-x\right\|})
derivative of f(x)=(3x^6+8x^3)^4	derivative\:f(x)=(3x^{6}+8x^{3})^{4}
derivative of 1/(x^2+a^2)	\frac{d}{dx}(\frac{1}{x^{2}+a^{2}})
inverse oflaplace 5/(s^8)	inverselaplace\:\frac{5}{s^{8}}
limit as x approaches 1 of in^4x+e^x	\lim\:_{x\to\:1}(in^{4}x+e^{x})
integral from 0 to pi/6 of sin^4(6x)	\int\:_{0}^{\frac{π}{6}}\sin^{4}(6x)dx
integral of ((x+4))/(x^3+3x^2-10x)	\int\:\frac{(x+4)}{x^{3}+3x^{2}-10x}dx
derivative of-6x^2	\frac{d}{dx}(-6x^{2})
y^'=(y+5)(x+2),y(0)=1	y^{\prime\:}=(y+5)(x+2),y(0)=1
inverse oflaplace (10)/((s)(s^2+8s+25))	inverselaplace\:\frac{10}{(s)(s^{2}+8s+25)}
integral of 3x^2sin(2x)	\int\:3x^{2}\sin(2x)dx

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