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Popular Calculus Problems

y^'=5ysin(4x)	y^{\prime\:}=5y\sin(4x)
integral of (-1)/(sqrt(x))	\int\:\frac{-1}{\sqrt{x}}dx
inverse oflaplace 1/(2s-5)	inverselaplace\:\frac{1}{2s-5}
derivative of ln(sin(3x))	\frac{d}{dx}(\ln(\sin(3x)))
derivative of x^{2/3}-x^{1/3}+4	\frac{d}{dx}(x^{\frac{2}{3}}-x^{\frac{1}{3}}+4)
d/(dy)(-y)	\frac{d}{dy}(-y)
integral of xe^{12x}	\int\:xe^{12x}dx
(\partial)/(\partial x)(-4sqrt(x))	\frac{\partial\:}{\partial\:x}(-4\sqrt{x})
integral of 1/(sqrt(2x-5))	\int\:\frac{1}{\sqrt{2x-5}}dx
(\partial)/(\partial x)(2zy)	\frac{\partial\:}{\partial\:x}(2zy)
area x=((y-4)^2)/4 ,y=7-x	area\:x=\frac{(y-4)^{2}}{4},y=7-x
derivative of-243sin(3x)	\frac{d}{dx}(-243\sin(3x))
derivative of ln(e^{3x})	derivative\:\ln(e^{3x})
laplacetransform (t^2-3)^2	laplacetransform\:(t^{2}-3)^{2}
derivative of (x+3/(x-2))	\frac{d}{dx}(\frac{x+3}{x-2})
(\partial)/(\partial x)(xy^3+2xy)	\frac{\partial\:}{\partial\:x}(xy^{3}+2xy)
limit as x approaches infinity of tan((2xpi)/(1+8x))	\lim\:_{x\to\:\infty\:}(\tan(\frac{2xπ}{1+8x}))
integral of 1/(sqrt(36x^2-49))	\int\:\frac{1}{\sqrt{36x^{2}-49}}dx
derivative of (4x/((x^2+2)^2))	\frac{d}{dx}(\frac{4x}{(x^{2}+2)^{2}})
(\partial)/(\partial z)(x^2+y^2+z^2)	\frac{\partial\:}{\partial\:z}(x^{2}+y^{2}+z^{2})
limit as x approaches 0+of x^{sin(2x)}	\lim\:_{x\to\:0+}(x^{\sin(2x)})
tangent of y=6+5x^2-2x^3	tangent\:y=6+5x^{2}-2x^{3}
derivative of sin(2xcos(3x))	\frac{d}{dx}(\sin(2x)\cos(3x))
(\partial)/(\partial x)(z^{xy})	\frac{\partial\:}{\partial\:x}(z^{xy})
y^{''}+9y=4csc^2(3x)	y^{\prime\:\prime\:}+9y=4\csc^{2}(3x)
tangent of f(x)=x^3-3x+2,(3,20)	tangent\:f(x)=x^{3}-3x+2,(3,20)
laplacetransform e^{2t+3}	laplacetransform\:e^{2t+3}
derivative of-cos(3x)	derivative\:-\cos(3x)
tangent of f(x)= 1/(sqrt(8x)),\at x=9	tangent\:f(x)=\frac{1}{\sqrt{8x}},\at\:x=9
(\partial)/(\partial x)(2x^3y^2+2y+4x)	\frac{\partial\:}{\partial\:x}(2x^{3}y^{2}+2y+4x)
integral of x^3sqrt(x^4+1)	\int\:x^{3}\sqrt{x^{4}+1}dx
(d^2y)/(dx^2)+a^2*y-e^{b-x}-1=0	\frac{d^{2}y}{dx^{2}}+a^{2}\cdot\:y-e^{b-x}-1=0
1/y dx-x/((ln(x))^3)dy=0	\frac{1}{y}dx-\frac{x}{(\ln(x))^{3}}dy=0
derivative of 1/(y^2)-3/(y^4)(y+5y^3)	derivative\:\frac{1}{y^{2}}-\frac{3}{y^{4}}(y+5y^{3})
integral of 3x^{-3}+sin(x)	\int\:3x^{-3}+\sin(x)dx
(dy)/(dx)= y/x+x/y	\frac{dy}{dx}=\frac{y}{x}+\frac{x}{y}
(\partial)/(\partial θ)(r(θ)*cos(θ))	\frac{\partial\:}{\partial\:θ}(r(θ)\cdot\:\cos(θ))
derivative of e^{rt}	derivative\:e^{rt}
integral from-pi to pi of sin^3(x)	\int\:_{-π}^{π}\sin^{3}(x)dx
limit as x approaches 0+of xln(tan(3x))	\lim\:_{x\to\:0+}(x\ln(\tan(3x)))
derivative of-(19)/((2x-5)^2)	derivative\:-\frac{19}{(2x-5)^{2}}
limit as x approaches-26.8 of-26.8	\lim\:_{x\to\:-26.8}(-26.8)
taylor 4/(x+2),0	taylor\:\frac{4}{x+2},0
limit as x approaches infinity of 10*e^{(-x)/2}+4	\lim\:_{x\to\:\infty\:}(10\cdot\:e^{\frac{-x}{2}}+4)
(dy)/(dx)=(4x)/(9y)	\frac{dy}{dx}=\frac{4x}{9y}
derivative of e^{-1x}	\frac{d}{dx}(e^{-1x})
slope ofintercept (-1,-2),(3,2)	slopeintercept\:(-1,-2),(3,2)
derivative of ln(x+p)	derivative\:\ln(x+p)
d/(dy)(-4y)	\frac{d}{dy}(-4y)
sec(x)dy+csc(y)dx=0	\sec(x)dy+\csc(y)dx=0
(\partial)/(\partial x)(ln(x^4+y))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}+y))
y^'=y(2-ty)	y^{\prime\:}=y(2-ty)
(\partial)/(\partial x)(2xy^2z-4xz^2)	\frac{\partial\:}{\partial\:x}(2xy^{2}z-4xz^{2})
derivative of y=(3(x-1))/(4xsqrt(x))	derivative\:y=\frac{3(x-1)}{4x\sqrt{x}}
integral of xsin((npix)/(10))	\int\:x\sin(\frac{nπx}{10})dx
derivative of f(t)=t^9-1	derivative\:f(t)=t^{9}-1
(\partial)/(\partial y)(9x^{6y})	\frac{\partial\:}{\partial\:y}(9x^{6y})
(\partial)/(\partial x)(2xcos(x^2+y^2))	\frac{\partial\:}{\partial\:x}(2x\cos(x^{2}+y^{2}))
(dy)/(dt)=yr(1000-y)	\frac{dy}{dt}=yr(1000-y)
area y=sec^2(x),y=8cos(x),-pi/3 , pi/3	area\:y=\sec^{2}(x),y=8\cos(x),-\frac{π}{3},\frac{π}{3}
integral from 1 to infinity of (ln(x))/(x^{3/2)}	\int\:_{1}^{\infty\:}\frac{\ln(x)}{x^{\frac{3}{2}}}dx
derivative of 1000(1+x/(12)^{60})	\frac{d}{dx}(1000(1+\frac{x}{12})^{60})
derivative of f(x)=(1-x)(x^2-7)^2	derivative\:f(x)=(1-x)(x^{2}-7)^{2}
tangent of f(x)=sqrt(x^2-x+9),\at x=1	tangent\:f(x)=\sqrt{x^{2}-x+9},\at\:x=1
inverse oflaplace (10)/(s(s^2+8s+25))	inverselaplace\:\frac{10}{s(s^{2}+8s+25)}
(\partial)/(\partial x)(xarctan(yz))	\frac{\partial\:}{\partial\:x}(x\arctan(yz))
limit as x approaches 0 of (sin(x/2))/x	\lim\:_{x\to\:0}(\frac{\sin(\frac{x}{2})}{x})
limit as x approaches infinity of (1+x)^{2/x}	\lim\:_{x\to\:\infty\:}((1+x)^{\frac{2}{x}})
y^{''}-4y^'+3y=0,y(0)=2,y^'(0)=3	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=0,y(0)=2,y^{\prime\:}(0)=3
integral from 0 to 2 of sqrt(5)	\int\:_{0}^{2}\sqrt{5}dx
(\partial)/(\partial x)(xy^9-x^2y)	\frac{\partial\:}{\partial\:x}(xy^{9}-x^{2}y)
limit as x approaches 6 of sqrt(x^2+13)	\lim\:_{x\to\:6}(\sqrt{x^{2}+13})
(dy)/(dx)=2xy^4	\frac{dy}{dx}=2xy^{4}
derivative of y=ln((9+e^x)/(9-e^x))	derivative\:y=\ln(\frac{9+e^{x}}{9-e^{x}})
limit as x approaches 3 of (x+3)/(x^2-9)	\lim\:_{x\to\:3}(\frac{x+3}{x^{2}-9})
inverse oflaplace (2s+2)/(s+10)	inverselaplace\:\frac{2s+2}{s+10}
limit as x approaches 1-of (-1)/((x-1)^{2/3)}	\lim\:_{x\to\:1-}(\frac{-1}{(x-1)^{\frac{2}{3}}})
(\partial)/(\partial y)(3x^2-2y^3+6xy^2-8)	\frac{\partial\:}{\partial\:y}(3x^{2}-2y^{3}+6xy^{2}-8)
area x^21,8	area\:x^{2}1,8
tangent of f(x)=(3x)/(x-2),\at a=4	tangent\:f(x)=\frac{3x}{x-2},\at\:a=4
limit as x approaches 4 of x-2	\lim\:_{x\to\:4}(x-2)
tangent of 2cos(x)+cos^2(x)	tangent\:2\cos(x)+\cos^{2}(x)
integral of (sin^2(x))/(sqrt(1+cos(x)))	\int\:\frac{\sin^{2}(x)}{\sqrt{1+\cos(x)}}dx
limit as x approaches-2-of 1/(x+2)	\lim\:_{x\to\:-2-}(\frac{1}{x+2})
integral of 3^x-sec^2(x)	\int\:3^{x}-\sec^{2}(x)dx
f(x)=9ln(x)	f(x)=9\ln(x)
integral of sqrt(x)(1-x)^2	\int\:\sqrt{x}(1-x)^{2}dx
(\partial)/(\partial x)((2xy^2)/(1+x^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{2xy^{2}}{1+x^{2}y^{2}})
tangent of y=(x^2-3)(x^3-2x),(-2,-4)	tangent\:y=(x^{2}-3)(x^{3}-2x),(-2,-4)
derivative of (log_{7}(x-x^2)/(x^3))	\frac{d}{dx}(\frac{\log_{7}(x-x^{2})}{x^{3}})
derivative of [x^2(x^2+5x)]^4	derivative\:[x^{2}(x^{2}+5x)]^{4}
taylor e^{x^4}	taylor\:e^{x^{4}}
limit as x approaches 3 of (x-1)^2	\lim\:_{x\to\:3}((x-1)^{2})
(d^2y)/(dx^2)-3(dy)/(dx)+2y=0	\frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y=0
x^{''}+9x=27,x(0)=4,x^'(0)=6	x^{\prime\:\prime\:}+9x=27,x(0)=4,x^{\prime\:}(0)=6
integral of (sqrt(1+\sqrt{x)})/x	\int\:\frac{\sqrt{1+\sqrt{x}}}{x}dx
sum from n=1 to infinity of (2n)/(5n-4)	\sum\:_{n=1}^{\infty\:}\frac{2n}{5n-4}
integral of (sqrt(x^2-4))/(x^6)	\int\:\frac{\sqrt{x^{2}-4}}{x^{6}}dx
tangent of y=x^3-3x^2+25	tangent\:y=x^{3}-3x^{2}+25
integral from 0 to pi of 9e^xsin(x)	\int\:_{0}^{π}9e^{x}\sin(x)dx

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