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Popular Calculus Problems

d/(dy)(3xy^2)	\frac{d}{dy}(3xy^{2})
(\partial)/(\partial x)((2x-y)^4)	\frac{\partial\:}{\partial\:x}((2x-y)^{4})
integral from 0 to pi of (pi-x)cos(nx)	\int\:_{0}^{π}(π-x)\cos(nx)dx
limit as x approaches 6 of sqrt(x-10)	\lim\:_{x\to\:6}(\sqrt{x-10})
y^{''}+5y^'-6y=0	y^{\prime\:\prime\:}+5y^{\prime\:}-6y=0
derivative of y=ln(2+x)+2/(2+x)	derivative\:y=\ln(2+x)+\frac{2}{2+x}
derivative of sqrt(6x-1)	derivative\:\sqrt{6x-1}
(\partial)/(\partial x)(sin(x)+pi*cos(y))	\frac{\partial\:}{\partial\:x}(\sin(x)+π\cdot\:\cos(y))
x(dy)/(dx)+2y=sin(x)	x\frac{dy}{dx}+2y=\sin(x)
integral of (e^{8sqrt(x)})/(sqrt(x))	\int\:\frac{e^{8\sqrt{x}}}{\sqrt{x}}dx
limit as x approaches 0 of csc^2(x)	\lim\:_{x\to\:0}(\csc^{2}(x))
integral of (sin(21x))/(1+cos^2(21x))	\int\:\frac{\sin(21x)}{1+\cos^{2}(21x)}dx
integral from 0 to 1 of x(1-x)	\int\:_{0}^{1}x(1-x)dx
area 6x^2,x^2+8	area\:6x^{2},x^{2}+8
limit as x approaches 0 of (14)/(tan(x))	\lim\:_{x\to\:0}(\frac{14}{\tan(x)})
integral of csc^2(0.1x)	\int\:\csc^{2}(0.1x)dx
laplacetransform Q	laplacetransform\:Q
limit as x approaches 0 of (ln(1+4x))/x	\lim\:_{x\to\:0}(\frac{\ln(1+4x)}{x})
integral of x^{11}sqrt(x^6+5)	\int\:x^{11}\sqrt{x^{6}+5}dx
derivative of ln(x-6)	derivative\:\ln(x-6)
x^2y^{''}-20y=0	x^{2}y^{\prime\:\prime\:}-20y=0
d/(dθ)({r}(θ)(1-cos(θ)))	\frac{d}{dθ}({r}(θ)(1-\cos(θ)))
derivative of ln((3x+1(x+2)^2))	\frac{d}{dx}(\ln((3x+1)(x+2)^{2}))
derivative of xsin(7/x)	\frac{d}{dx}(x\sin(\frac{7}{x}))
derivative of e^{-2x}cos(x)	\frac{d}{dx}(e^{-2x}\cos(x))
tangent of y=3+4x+7xe^x	tangent\:y=3+4x+7xe^{x}
x^2y^{''}+3xy^'-35y=0	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}-35y=0
integral of tan(x)(4cos(x)+8sec(x))	\int\:\tan(x)(4\cos(x)+8\sec(x))dx
integral of (8x)/(1+x^2)	\int\:\frac{8x}{1+x^{2}}dx
(dy)/(dx)+y^5x+6y=0	\frac{dy}{dx}+y^{5}x+6y=0
integral of 1/(x^2sqrt(4-x^2))	\int\:\frac{1}{x^{2}\sqrt{4-x^{2}}}dx
derivative of 3xe^x-cos(x)	\frac{d}{dx}(3xe^{x}-\cos(x))
derivative of f(t)=sqrt(5-t)	derivative\:f(t)=\sqrt{5-t}
(ln(1+2x))^'	(\ln(1+2x))^{\prime\:}
(\partial)/(\partial x)(sqrt(x^2+3y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+3y^{2}})
integral of 1/((36-x^2)^{3/2)}	\int\:\frac{1}{(36-x^{2})^{\frac{3}{2}}}dx
derivative of (4t^5-6t)^8	derivative\:(4t^{5}-6t)^{8}
(\partial)/(\partial x)(sin(pi(x-5y)))	\frac{\partial\:}{\partial\:x}(\sin(π(x-5y)))
derivative of cosh(xsinh(x))	\frac{d}{dx}(\cosh(x)\sinh(x))
derivative of (((-2x-1)/((-4x+2)))^5)	\frac{d}{dx}((\frac{(-2x-1)}{(-4x+2)})^{5})
derivative of 1/(x^{2/3)}	derivative\:\frac{1}{x^{\frac{2}{3}}}
inverse oflaplace 6/(s(s+2))	inverselaplace\:\frac{6}{s(s+2)}
derivative of 3x^2-8x-sqrt(x)	derivative\:3x^{2}-8x-\sqrt{x}
derivative of f(x)=ln(3x^3+2)	derivative\:f(x)=\ln(3x^{3}+2)
integral of x/((x^2+z^2)^{3/2)}	\int\:\frac{x}{(x^{2}+z^{2})^{\frac{3}{2}}}dx
(\partial)/(\partial y)(xe^{xy}+y^2sin(xy))	\frac{\partial\:}{\partial\:y}(xe^{xy}+y^{2}\sin(xy))
(\partial)/(\partial x)(ln(x^7+y^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{7}+y^{4}))
integral of cot(θ/3)	\int\:\cot(\frac{θ}{3})dθ
inverse oflaplace 2/(s^3)	inverselaplace\:\frac{2}{s^{3}}
derivative of cos^x(x)	derivative\:\cos^{x}(x)
integral from 0 to pi/2 of-2cos^5(x)	\int\:_{0}^{\frac{π}{2}}-2\cos^{5}(x)dx
derivative of (6z+e^{-z^2})^3	derivative\:(6z+e^{-z^{2}})^{3}
(\partial)/(\partial x)(2ysin(10x-y))	\frac{\partial\:}{\partial\:x}(2y\sin(10x-y))
((x^2)/(2x+4))^'	(\frac{x^{2}}{2x+4})^{\prime\:}
derivative of cot(pi/4)	\frac{d}{dx}(\cot(\frac{π}{4}))
integral of cos(-4x)	\int\:\cos(-4x)dx
integral of 1/(1+e^{4x)}	\int\:\frac{1}{1+e^{4x}}dx
derivative of (3x^2-6x+6)e^x	derivative\:(3x^{2}-6x+6)e^{x}
inverse oflaplace ((s+5))/((s^2+5s+6))	inverselaplace\:\frac{(s+5)}{(s^{2}+5s+6)}
integral of e^{-x}(2-x)	\int\:e^{-x}(2-x)dx
derivative of ln(tan(4x))	derivative\:\ln(\tan(4x))
integral of 1/(sqrt(u+3))	\int\:\frac{1}{\sqrt{u+3}}du
derivative of (x^4-3x^2)	\frac{d}{dx}((x^{4}-3x)^{2})
x^2y^{''}+2xy^'-2y=x^2ln(x)	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-2y=x^{2}\ln(x)
laplacetransform 1/4*sin(2t)	laplacetransform\:\frac{1}{4}\cdot\:\sin(2t)
derivative of (e^xx-e^x/(7x^2))	\frac{d}{dx}(\frac{e^{x}x-e^{x}}{7x^{2}})
(\partial)/(\partial y)(sin(x-y)+(x-y))	\frac{\partial\:}{\partial\:y}(\sin(x-y)+(x-y))
derivative of sqrt(x)-3e^x	\frac{d}{dx}(\sqrt{x}-3e^{x})
integral of 2sin(x)cos(x)	\int\:2\sin(x)\cos(x)dx
(\partial)/(\partial x)(ln(x^2+3))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+3))
limit as x approaches 2 of (2x-4)/(x-2)	\lim\:_{x\to\:2}(\frac{2x-4}{x-2})
(3x^2+y-4)-(2y-x)(dy)/(dx)=0	(3x^{2}+y-4)-(2y-x)\frac{dy}{dx}=0
integral of 3ln(x)	\int\:3\ln(x)dx
integral of e^{ln(sqrt(x))}	\int\:e^{\ln(\sqrt{x})}dx
(\partial)/(\partial y)(x^5ln(y^6))	\frac{\partial\:}{\partial\:y}(x^{5}\ln(y^{6}))
xy^'+y=3xy^2,y(1)=9	xy^{\prime\:}+y=3xy^{2},y(1)=9
integral of (1+x^2)/(x^2)	\int\:\frac{1+x^{2}}{x^{2}}dx
integral of 24sec^4(x)	\int\:24\sec^{4}(x)dx
derivative of 1-e^{-x/(50})	\frac{d}{dx}(1-e^{-\frac{x}{50}})
tangent of f(x)=(2x)/(e^{3x^2)},\at x=-1	tangent\:f(x)=\frac{2x}{e^{3x^{2}}},\at\:x=-1
integral of 1/(sqrt(2+3y^2))	\int\:\frac{1}{\sqrt{2+3y^{2}}}dy
integral of 6/(2+3x)	\int\:\frac{6}{2+3x}dx
integral of csc^{11}(x)	\int\:\csc^{11}(x)dx
integral of-2x+3	\int\:-2x+3dx
derivative of sqrt(2x+2)	\frac{d}{dx}(\sqrt{2x+2})
integral of x/(e^{-2x)}	\int\:\frac{x}{e^{-2x}}dx
integral of 1/(u^2+2)	\int\:\frac{1}{u^{2}+2}du
integral from 0 to 1 of e^ssin(t-s)	\int\:_{0}^{1}e^{s}\sin(t-s)ds
tangent of f(x)=x^3-9x,\at x=(-3)	tangent\:f(x)=x^{3}-9x,\at\:x=(-3)
tangent of f(x)=2x-1/x ,\at x=0.5	tangent\:f(x)=2x-\frac{1}{x},\at\:x=0.5
limit as x approaches 1+of 5/(x-1)	\lim\:_{x\to\:1+}(\frac{5}{x-1})
integral of (e^{5x})/((e^{5x)+11)^2}	\int\:\frac{e^{5x}}{(e^{5x}+11)^{2}}dx
y^{'''}-y^{''}+2y^'+4y=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+2y^{\prime\:}+4y=0
integral from-1 to 1 of e^xcos(x)	\int\:_{-1}^{1}e^{x}\cos(x)dx
derivative of x^{9/5}y^7z^{2/7}	\frac{d}{dx}(x^{\frac{9}{5}}y^{7}z^{\frac{2}{7}})
y^'= 1/10 y(500-y)	y^{\prime\:}=\frac{1}{10}y(500-y)
taylor x^5,x=2	taylor\:x^{5},x=2
tangent of y=x^2+3x+11	tangent\:y=x^{2}+3x+11
taylor 3/(1+3x)	taylor\:\frac{3}{1+3x}
integral of xsqrt(5+2x)	\int\:x\sqrt{5+2x}dx

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