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Popular Calculus Problems

(\partial)/(\partial x)(6y^2)	\frac{\partial\:}{\partial\:x}(6y^{2})
derivative of f(x)=(3x^2-5x)e^x	derivative\:f(x)=(3x^{2}-5x)e^{x}
derivative of f(t)=(t^{62}+3t+3)(5t^2+4)	derivative\:f(t)=(t^{62}+3t+3)(5t^{2}+4)
derivative of sqrt(ln(7x))	\frac{d}{dx}(\sqrt{\ln(7x)})
(\partial)/(\partial x)((xy-1)^2)	\frac{\partial\:}{\partial\:x}((xy-1)^{2})
integral of (x^4+4)/(x^3)	\int\:\frac{x^{4}+4}{x^{3}}dx
y^{''}+3y^'+2y=e^{-2t}	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=e^{-2t}
integral of (x^2)/(sqrt((x^2+a^2)^3))	\int\:\frac{x^{2}}{\sqrt{(x^{2}+a^{2})^{3}}}dx
(sin(x)sin(2x)sin(3x))^'	(\sin(x)\sin(2x)\sin(3x))^{\prime\:}
derivative of y=e^xsin(2x)	derivative\:y=e^{x}\sin(2x)
limit as x approaches 0+of xln(sin(x))	\lim\:_{x\to\:0+}(x\ln(\sin(x)))
integral of 1/(sqrt(5x-2))	\int\:\frac{1}{\sqrt{5x-2}}dx
(dr)/(dθ)=8(cos(θ/3))^3	\frac{dr}{dθ}=8(\cos(\frac{θ}{3}))^{3}
limit as x approaches 0+of (e^x+x)^{2/x}	\lim\:_{x\to\:0+}((e^{x}+x)^{\frac{2}{x}})
derivative of ((x+1/(x-1))^{1/2})	\frac{d}{dx}((\frac{x+1}{x-1})^{\frac{1}{2}})
integral of 1/(sqrt(3x^2+4x+5))	\int\:\frac{1}{\sqrt{3x^{2}+4x+5}}dx
derivative of-ax	\frac{d}{dx}(-ax)
(\partial)/(\partial x)(cos(8x)sin(3y))	\frac{\partial\:}{\partial\:x}(\cos(8x)\sin(3y))
derivative of x^2(e^x)	\frac{d}{dx}(x^{2}(e^{x}))
limit as h approaches 0 of ((sqrt(16+h))-4)/h	\lim\:_{h\to\:0}(\frac{(\sqrt{16+h})-4}{h})
integral of x(4+x^2)^{10}	\int\:x(4+x^{2})^{10}dx
limit as x approaches 1+of 5x+2p(x)	\lim\:_{x\to\:1+}(5x+2p(x))
(x+3)(dy)/(dx)+y=ln(x)	(x+3)\frac{dy}{dx}+y=\ln(x)
derivative of x^2(1-2x)	derivative\:x^{2}(1-2x)
(1-x)(dy)/(dx)-xy=x+x^2	(1-x)\frac{dy}{dx}-xy=x+x^{2}
derivative of (4x-1^2)	\frac{d}{dx}((4x-1)^{2})
area y=x^2,y=2x^2-4x,y=0	area\:y=x^{2},y=2x^{2}-4x,y=0
integral of (x^2)/((x^2+8)^{3/2)}	\int\:\frac{x^{2}}{(x^{2}+8)^{\frac{3}{2}}}dx
tangent of x^3-8x	tangent\:x^{3}-8x
integral of 18x^{1/2}	\int\:18x^{\frac{1}{2}}dx
(\partial)/(\partial x)(-1/((x-y)^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{(x-y)^{2}})
f(y)=cos(y)	f(y)=\cos(y)
integral from 0 to 5 of (x/(sqrt(x+4)))	\int\:_{0}^{5}(\frac{x}{\sqrt{x+4}})dx
y^'+y+1=0	y^{\prime\:}+y+1=0
derivative of (1+xcos(x))	\frac{d}{dx}((1+x)\cos(x))
derivative of f(t)=cos^2(e^{cos^2(t)})	derivative\:f(t)=\cos^{2}(e^{\cos^{2}(t)})
integral of (19)/(x^2+1)	\int\:\frac{19}{x^{2}+1}dx
(\partial)/(\partial x)(7e^x)	\frac{\partial\:}{\partial\:x}(7e^{x})
integral of x/(x-2)	\int\:\frac{x}{x-2}dx
y^'=(x-2)/(y+1)	y^{\prime\:}=\frac{x-2}{y+1}
integral of-\|x\|^2	\int\:-\left\|x\right\|^{2}dx
integral from 0 to 1 of 4ln(x)	\int\:_{0}^{1}4\ln(x)dx
slope derivative of 5/(4x)-7/4	slope\:\frac{d}{dx}(\frac{5}{4x})-\frac{7}{4}
integral of ((arctan(x))^3)/(1+x^2)	\int\:\frac{(\arctan(x))^{3}}{1+x^{2}}dx
(\partial)/(\partial x)(x/(x^2+(y-1)^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+(y-1)^{2}})
integral of 1/(12x)	\int\:\frac{1}{12x}dx
derivative of log_{5}(x^2-7x)	\frac{d}{dx}(\log_{5}(x^{2}-7x))
v'=-0.01v^2	v\prime\:=-0.01v^{2}
y^{''}+2y^'+2y=sin(1t)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(1t)
limit as x approaches 5 of-2	\lim\:_{x\to\:5}(-2)
derivative of f(x)=x^2+8	derivative\:f(x)=x^{2}+8
integral of 4x^{1/3}-4x^{-1/3}	\int\:4x^{\frac{1}{3}}-4x^{-\frac{1}{3}}dx
integral of-(sin(x))^2	\int\:-(\sin(x))^{2}dx
f(t)=2sin^2(t)	f(t)=2\sin^{2}(t)
integral from-pi to pi of cos^2(5x)	\int\:_{-π}^{π}\cos^{2}(5x)dx
limit as x approaches pi/2+of 1/x sec(x)	\lim\:_{x\to\:\frac{π}{2}+}(\frac{1}{x}\sec(x))
limit as x approaches 1 of \|x-2\|	\lim\:_{x\to\:1}(\left\|x-2\right\|)
integral of tan(x)sec^3(x)	\int\:\tan(x)\sec^{3}(x)dx
integral of x/(x+	\int\:\frac{x}{x+d}dx
(\partial)/(\partial x)(x^3-2xy+y^2+3)	\frac{\partial\:}{\partial\:x}(x^{3}-2xy+y^{2}+3)
y^{'''}=0	y^{\prime\:\prime\:\prime\:}=0
inverse oflaplace 4/(5s)	inverselaplace\:\frac{4}{5s}
integral of (\sqrt[6]{x}+\sqrt[7]{x})	\int\:(\sqrt[6]{x}+\sqrt[7]{x})dx
4y^{''}+12y^'+9y=0,y(0)=1,y^'(0)=-5	4y^{\prime\:\prime\:}+12y^{\prime\:}+9y=0,y(0)=1,y^{\prime\:}(0)=-5
derivative of sqrt(x)sin(x)	derivative\:\sqrt{x}\sin(x)
derivative of f(x)=sqrt(1+8x)	derivative\:f(x)=\sqrt{1+8x}
derivative of (1+x^4)^{2/3}	derivative\:(1+x^{4})^{\frac{2}{3}}
(\partial)/(\partial x)(y(-14x-4y+1))	\frac{\partial\:}{\partial\:x}(y(-14x-4y+1))
integral of x(x^2+3)^2	\int\:x(x^{2}+3)^{2}dx
integral of 2/(x^{1/2)}	\int\:\frac{2}{x^{\frac{1}{2}}}dx
2x+3y+(6x+9y-3)y^'=0	2x+3y+(6x+9y-3)y^{\prime\:}=0
derivative of f(x)=cos(x^2)-2x^2sin(x^2)	derivative\:f(x)=\cos(x^{2})-2x^{2}\sin(x^{2})
(\partial)/(\partial y)((x+y)(x-y))	\frac{\partial\:}{\partial\:y}((x+y)(x-y))
derivative of x^e+1/(x^{sqrt(10)})	\frac{d}{dx}(x^{e}+\frac{1}{x^{\sqrt{10}}})
(d^2)/(dx^2)((4x^2+8x)cos(x))	\frac{d^{2}}{dx^{2}}((4x^{2}+8x)\cos(x))
inverse oflaplace a/(s^2+a^2)	inverselaplace\:\frac{a}{s^{2}+a^{2}}
(x^2)/(y^2-2)(dy)/(dx)= 1/(2y)	\frac{x^{2}}{y^{2}-2}\frac{dy}{dx}=\frac{1}{2y}
integral from-10 to 10 of (x^2+x)	\int\:_{-10}^{10}(x^{2}+x)dx
derivative of x(1-2x^3)	\frac{d}{dx}(x(1-2x)^{3})
integral from-1 to 2 of 1/(x^5)	\int\:_{-1}^{2}\frac{1}{x^{5}}dx
derivative of-4/(x^3)	derivative\:-\frac{4}{x^{3}}
integral of 2(x+y)	\int\:2(x+y)dx
(d^2)/(dx^2)(xsin(x))	\frac{d^{2}}{dx^{2}}(x\sin(x))
(\partial)/(\partial x)(cos(y^2-2x))	\frac{\partial\:}{\partial\:x}(\cos(y^{2}-2x))
derivative of (x+1)/(x-1)	derivative\:\frac{x+1}{x-1}
(\partial)/(\partial x)(log_{10}(xy))	\frac{\partial\:}{\partial\:x}(\log_{10}(xy))
area y=x^2-2x,y=-x^2+4x	area\:y=x^{2}-2x,y=-x^{2}+4x
limit as x approaches 2+of 3/(x^2-4)	\lim\:_{x\to\:2+}(\frac{3}{x^{2}-4})
sum from n=1 to infinity of 1/(n^4+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{4}+1}
(\partial)/(\partial x)(1/(x+4y))	\frac{\partial\:}{\partial\:x}(\frac{1}{x+4y})
integral of 28t(7t^2-5)^3	\int\:28t(7t^{2}-5)^{3}dt
(\partial)/(\partial y)((2x)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{2x}{x^{2}+y^{2}})
integral of (x^2)/((16+x^2)^2)	\int\:\frac{x^{2}}{(16+x^{2})^{2}}dx
integral of (8x-7)*ln(x)	\int\:(8x-7)\cdot\:\ln(x)dx
area xsqrt(8-2x^2),0,2	area\:x\sqrt{8-2x^{2}},0,2
derivative of \sqrt[4]{(4x)/(4x-3)}	derivative\:\sqrt[4]{\frac{4x}{4x-3}}
(\partial)/(\partial x)(ln(x/y))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{y}))
integral from-a to a of e^{(-x^2)/(a^2)}	\int\:_{-a}^{a}e^{\frac{-x^{2}}{a^{2}}}dx
slope of (-4,3),(3,1)	slope\:(-4,3),(3,1)
integral of (x^2-15)/(x+7)	\int\:\frac{x^{2}-15}{x+7}dx

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