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Popular Calculus Problems

derivative of e^{\|x\|}	\frac{d}{dx}(e^{\left\|x\right\|})
(\partial)/(\partial x)(cos(x+2y))	\frac{\partial\:}{\partial\:x}(\cos(x+2y))
tangent of y=(x^3-9x)^8,(3,0)	tangent\:y=(x^{3}-9x)^{8},(3,0)
x^2y^{''}-2xy^'+2y=x^2+2	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}+2y=x^{2}+2
derivative of (0.9e^x/(tan(x)))	\frac{d}{dx}(\frac{0.9e^{x}}{\tan(x)})
(x^{1/3})^'	(x^{\frac{1}{3}})^{\prime\:}
derivative of 3t^3-2/(t^2)	derivative\:3t^{3}-\frac{2}{t^{2}}
tangent of f(x)=x^2-6	tangent\:f(x)=x^{2}-6
integral from 0 to infinity of 77(e^x)/(e^{2x)+3}	\int\:_{0}^{\infty\:}77\frac{e^{x}}{e^{2x}+3}dx
y*y^'=1	y\cdot\:y^{\prime\:}=1
integral of 1/(sqrt(1-4^2))	\int\:\frac{1}{\sqrt{1-4^{2}}}dx
integral from-4 to 4 of (sqrt(16-x^2))	\int\:_{-4}^{4}(\sqrt{16-x^{2}})dx
y^'= x/(x-1),y(2)=5	y^{\prime\:}=\frac{x}{x-1},y(2)=5
integral of x/(sqrt(x^2-8x))	\int\:\frac{x}{\sqrt{x^{2}-8x}}dx
derivative of 5xsin(x)	\frac{d}{dx}(5x\sin(x))
derivative of \sqrt[3]{x-2}	derivative\:\sqrt[3]{x-2}
derivative of 3x^2-2x+4	\frac{d}{dx}(3x^{2}-2x+4)
(\partial)/(\partial y)(y(1-x^2))	\frac{\partial\:}{\partial\:y}(y(1-x^{2}))
limit as x approaches 1 of (2x+3)/(x+1)	\lim\:_{x\to\:1}(\frac{2x+3}{x+1})
(\partial}{\partial y}(166x+456y-\frac{5000)/x-(1080)/y+43590)	\frac{\partial\:}{\partial\:y}(166x+456y-\frac{5000}{x}-\frac{1080}{y}+43590)
integral of 6xcsc(6x)cot(6x)	\int\:6x\csc(6x)\cot(6x)dx
tangent of f(x)=(64)/(x^2+16),\at x=-4	tangent\:f(x)=\frac{64}{x^{2}+16},\at\:x=-4
derivative of 5e^{-t}	derivative\:5e^{-t}
derivative of sqrt(arcsin(x))	\frac{d}{dx}(\sqrt{\arcsin(x)})
limit as x approaches-1 of 1-x^2	\lim\:_{x\to\:-1}(1-x^{2})
tangent of y=x^2-2x,\at x=0	tangent\:y=x^{2}-2x,\at\:x=0
integral of (ln(x))/(xsqrt(1+7ln^2(x)))	\int\:\frac{\ln(x)}{x\sqrt{1+7\ln^{2}(x)}}dx
(dy)/(dx)=2y-7y^3	\frac{dy}{dx}=2y-7y^{3}
derivative of (sqrt(x)^{5x})	\frac{d}{dx}((\sqrt{x})^{5x})
integral of (x^3+x+4)/(x^2)	\int\:\frac{x^{3}+x+4}{x^{2}}dx
d/(dy)(arctan(x/y))	\frac{d}{dy}(\arctan(\frac{x}{y}))
derivative of \sqrt[8]{x^9}	\frac{d}{dx}(\sqrt[8]{x^{9}})
derivative of arctan(x^4)	\frac{d}{dx}(\arctan(x^{4}))
f(t)=sqrt((t^2+1)/(t^2-1))	f(t)=\sqrt{\frac{t^{2}+1}{t^{2}-1}}
integral from 1 to infinity of 1/(5x+2)	\int\:_{1}^{\infty\:}\frac{1}{5x+2}dx
derivative of log_{7}(x^2)	\frac{d}{dx}(\log_{7}(x^{2}))
derivative of (x^2-y^2/(x^2+y^2))	\frac{d}{dx}(\frac{x^{2}-y^{2}}{x^{2}+y^{2}})
derivative of 6(2x-9^5)	\frac{d}{dx}(6(2x-9)^{5})
(5x+ye^{(y/x)})dx-xe^{y/x}dy=0	(5x+ye^{(\frac{y}{x})})dx-xe^{\frac{y}{x}}dy=0
(\partial)/(\partial x)(ln(cos(xy)+2))	\frac{\partial\:}{\partial\:x}(\ln(\cos(xy)+2))
integral of tan^4(x)+tan^6(x)	\int\:\tan^{4}(x)+\tan^{6}(x)dx
limit as h approaches 0 of 1/(5-h)	\lim\:_{h\to\:0}(\frac{1}{5-h})
inverse oflaplace (e^{-2s})/(s(s-1))	inverselaplace\:\frac{e^{-2s}}{s(s-1)}
derivative of-2x+2	\frac{d}{dx}(-2x+2)
integral of 13sqrt(tan(x))sec^4(x)	\int\:13\sqrt{\tan(x)}\sec^{4}(x)dx
derivative of (x^7+5x)^{1/3}	derivative\:(x^{7}+5x)^{\frac{1}{3}}
derivative of x^2ln(x^3)	\frac{d}{dx}(x^{2}\ln(x^{3}))
f(x)=ln(1-x^2)	f(x)=\ln(1-x^{2})
(\partial)/(\partial y)(e^{2xy})	\frac{\partial\:}{\partial\:y}(e^{2xy})
derivative of e^6	\frac{d}{dx}(e^{6})
sum from k=0 to infinity of k/(3^k)	\sum\:_{k=0}^{\infty\:}\frac{k}{3^{k}}
simplify 1sin(x)+xcos(x)	simplify\:1\cdot\:\sin(x)+x\cdot\:\cos(x)
sin(5x)y^'=0	\sin(5x)y^{\prime\:}=0
derivative of f(x)=sqrt(7)x+sqrt(10x)	derivative\:f(x)=\sqrt{7}x+\sqrt{10x}
f^{''}(x)=2,f^'(2)=5,f(3)=2	f^{\prime\:\prime\:}(x)=2,f^{\prime\:}(2)=5,f(3)=2
(\partial)/(\partial x)(36x^8y^5+8x^7y^3)	\frac{\partial\:}{\partial\:x}(36x^{8}y^{5}+8x^{7}y^{3})
limit as x approaches 0+of (e^x+x)^{4/x}	\lim\:_{x\to\:0+}((e^{x}+x)^{\frac{4}{x}})
integral from 0 to 1 of 4(1+sqrt(x))^8	\int\:_{0}^{1}4(1+\sqrt{x})^{8}dx
integral of 0.6x^2-4.4x+60	\int\:0.6x^{2}-4.4x+60dx
integral of (x+2)/(x+3)	\int\:\frac{x+2}{x+3}dx
-10x^2y+y^'=9x^2	-10x^{2}y+y^{\prime\:}=9x^{2}
integral of 1/(3^x+1)	\int\:\frac{1}{3^{x}+1}dx
y^{''}-6y^'+9y=0,y(0)=-3,y^'(0)=5	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=-3,y^{\prime\:}(0)=5
(dy)/(dx)=(x+1)^2	\frac{dy}{dx}=(x+1)^{2}
integral from 1 to 3 of (x+2)(x-1)^5	\int\:_{1}^{3}(x+2)(x-1)^{5}dx
derivative of (-x^2-4x-1/(4x-3))	\frac{d}{dx}(\frac{-x^{2}-4x-1}{4x-3})
integral of e^{x^3+1}x^2	\int\:e^{x^{3}+1}x^{2}dx
derivative of sqrt(ln(e^{3x)+e^{-3x}})	\frac{d}{dx}(\sqrt{\ln(e^{3x}+e^{-3x})})
derivative of ln((x+3)/(sqrt(x-1)))	derivative\:\ln(\frac{x+3}{\sqrt{x-1}})
derivative of 5sec(4x)	\frac{d}{dx}(5\sec(4x))
integral of (3x^2+y^2)ln(x^2+y^2)	\int\:(3x^{2}+y^{2})\ln(x^{2}+y^{2})dx
integral of (x(x+2))/(x^3+3x^2-4)	\int\:\frac{x(x+2)}{x^{3}+3x^{2}-4}dx
integral of 1/(sqrt(e^{2x)-6)}	\int\:\frac{1}{\sqrt{e^{2x}-6}}dx
integral of 15sin^{-3/2}(x)cos^3(x)	\int\:15\sin^{-\frac{3}{2}}(x)\cos^{3}(x)dx
integral of ln^6(x)	\int\:\ln^{6}(x)dx
integral of sin(3x-5)	\int\:\sin(3x-5)dx
integral of 1/(\sqrt[4]{5-x)+sqrt(5-x)}	\int\:\frac{1}{\sqrt[4]{5-x}+\sqrt{5-x}}dx
d/(dθ)(5/(sin(θ)-2cos(θ)))	\frac{d}{dθ}(\frac{5}{\sin(θ)-2\cos(θ)})
x^2(dy)/(dx)=x-xy	x^{2}\frac{dy}{dx}=x-xy
y^'=9x+y,y(0)=8	y^{\prime\:}=9x+y,y(0)=8
inverse oflaplace 1/((s^2+2^2))	inverselaplace\:\frac{1}{(s^{2}+2^{2})}
integral of x^2-6x	\int\:x^{2}-6xdx
derivative of-1/3 x^2	derivative\:-\frac{1}{3}x^{2}
derivative of ln(9x^2-11)	\frac{d}{dx}(\ln(9x^{2}-11))
(tcos(t))^'	(t\cos(t))^{\prime\:}
integral of (x-1)(x+2)(x-3)	\int\:(x-1)(x+2)(x-3)dx
derivative of f(x)=(4x)/(x^3+5)	derivative\:f(x)=\frac{4x}{x^{3}+5}
integral of (80)/(64-x^2)	\int\:\frac{80}{64-x^{2}}dx
(\partial)/(\partial x)({f}(x,b,y)(ax+by))	\frac{\partial\:}{\partial\:x}({f}(x,b,y)(ax+by))
area 5x, 1/7 x,50-x^2	area\:5x,\frac{1}{7}x,50-x^{2}
(x^2+1)y^'+7x(y-1)=0,y(0)=4	(x^{2}+1)y^{\prime\:}+7x(y-1)=0,y(0)=4
limit as x approaches infinity of cos(0)	\lim\:_{x\to\:\infty\:}(\cos(0))
derivative of sin(x)+5/8 cot(x)	derivative\:\sin(x)+\frac{5}{8}\cot(x)
limit as x approaches-6 of x^2-1	\lim\:_{x\to\:-6}(x^{2}-1)
sum from n=1 to infinity of 1/(e^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{1}{e^{2n}}
(12-20y+e^{-5x})dx-4dy=0	(12-20y+e^{-5x})dx-4dy=0
integral of 8x^{1/3}+8x^{-1/3}	\int\:8x^{\frac{1}{3}}+8x^{-\frac{1}{3}}dx
integral from 0 to 2 of ln(2x)	\int\:_{0}^{2}\ln(2x)dx
(\partial)/(\partial x)(y/(ln(x-1)))	\frac{\partial\:}{\partial\:x}(\frac{y}{\ln(x-1)})
(dy)/(dt)+ay=0	\frac{dy}{dt}+ay=0

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