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Popular Calculus Problems

derivative of cos(x-x)	\frac{d}{dx}(\cos(x)-x)
tangent of (x-5)^2+(y-3)^2=18,(8,6)	tangent\:(x-5)^{2}+(y-3)^{2}=18,(8,6)
integral from 0 to 4 of pi(3x)^2	\int\:_{0}^{4}π(3x)^{2}dx
derivative of f(x)=cos(tan(x))	derivative\:f(x)=\cos(\tan(x))
y^{''}+ay^'+by=t+e^{3t}	y^{\prime\:\prime\:}+ay^{\prime\:}+by=t+e^{3t}
limit as x approaches-1 of ln(x+1)	\lim\:_{x\to\:-1}(\ln(x+1))
(\partial)/(\partial x)(1/2 (x^2+4y^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}(x^{2}+4y^{2}))
(\partial)/(\partial x)(1/(sqrt(2x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{2x}})
2xy(dy)/(dx)=y^2-x^2+1	2xy\frac{dy}{dx}=y^{2}-x^{2}+1
tangent of 100x^2+400x+5000,0.5	tangent\:100x^{2}+400x+5000,0.5
integral of e^{y(1-x)}	\int\:e^{y(1-x)}dx
derivative of y=7x^2cos(x)cot(x)	\frac{d}{dx}y=7x^{2}\cos(x)\cot(x)
(dy)/(dx)+e^xy=-9e^x	\frac{dy}{dx}+e^{x}y=-9e^{x}
tangent of f(x)=(6x)/(x-1),(-1,3)	tangent\:f(x)=\frac{6x}{x-1},(-1,3)
integral of ((2x^3+3x))/(x^4+3x^2+7)	\int\:\frac{(2x^{3}+3x)}{x^{4}+3x^{2}+7}dx
(\partial)/(\partial x)(4xcos(4xy))	\frac{\partial\:}{\partial\:x}(4x\cos(4xy))
limit as x approaches 0 of (sin(20x))/x	\lim\:_{x\to\:0}(\frac{\sin(20x)}{x})
limit as x approaches 2+of-1/(x^2-4)	\lim\:_{x\to\:2+}(-\frac{1}{x^{2}-4})
integral of (tan(θ)sec(θ))	\int\:(\tan(θ)\sec(θ))dθ
integral of (1-cos(x))/(1+cos(x))	\int\:\frac{1-\cos(x)}{1+\cos(x)}dx
integral of e^{2x-7}	\int\:e^{2x-7}dx
derivative of 4arcsin(x^3)	\frac{d}{dx}(4\arcsin(x^{3}))
derivative of 2/(\sqrt[3]{x^2)}	derivative\:\frac{2}{\sqrt[3]{x^{2}}}
derivative of (4csc(x)/(5^x))	\frac{d}{dx}(\frac{4\csc(x)}{5^{x}})
limit as x approaches infinity of n/(n!)	\lim\:_{x\to\:\infty\:}(\frac{n}{n!})
derivative of ln(49sin^2(x))	derivative\:\ln(49\sin^{2}(x))
y^{''}+10y^'+27y=0	y^{\prime\:\prime\:}+10y^{\prime\:}+27y=0
(\partial)/(\partial v)(v^2)	\frac{\partial\:}{\partial\:v}(v^{2})
f(x)=(25)/x	f(x)=\frac{25}{x}
integral of 5sin(sqrt(x))	\int\:5\sin(\sqrt{x})dx
derivative of sqrt(x^2+y)	\frac{d}{dx}(\sqrt{x^{2}+y})
d/(dy)(t/(2y^4))	\frac{d}{dy}(\frac{t}{2y^{4}})
integral of 1/(sqrt(64x^2+1))	\int\:\frac{1}{\sqrt{64x^{2}+1}}dx
6x^2((dy)/(dx))=((dy)/(dx))+9xe^{-y}	6x^{2}(\frac{dy}{dx})=(\frac{dy}{dx})+9xe^{-y}
integral of 8x^{-3}	\int\:8x^{-3}dx
integral from 0 to 2 of e^{-x}	\int\:_{0}^{2}e^{-x}dx
integral of sqrt(3+x^2)	\int\:\sqrt{3+x^{2}}dx
integral of (3x^2-9x+2)	\int\:(3x^{2}-9x+2)dx
derivative of sqrt(3x+9)	\frac{d}{dx}(\sqrt{3x+9})
integral of sqrt((1+cos(x))/(1-cos(x)))	\int\:\sqrt{\frac{1+\cos(x)}{1-\cos(x)}}dx
derivative of arcsin(5x)	\frac{d}{dx}(\arcsin(5x))
derivative of 3/5 x^{5/3}-3/4 x^{1/3}+9	derivative\:\frac{3}{5}x^{\frac{5}{3}}-\frac{3}{4}x^{\frac{1}{3}}+9
limit as x approaches-2+of (1-x)/(x^3+8)	\lim\:_{x\to\:-2+}(\frac{1-x}{x^{3}+8})
limit as x approaches 1-of 2/(x-1)	\lim\:_{x\to\:1-}(\frac{2}{x-1})
(\partial)/(\partial x)((3x^2+y)e^{xy^2})	\frac{\partial\:}{\partial\:x}((3x^{2}+y)e^{xy^{2}})
laplacetransform (e^{2t}-e^t+t)^2	laplacetransform\:(e^{2t}-e^{t}+t)^{2}
derivative of 2x^2-7x-195	derivative\:2x^{2}-7x-195
integral of-cos((pit)/4)	\int\:-\cos(\frac{πt}{4})dt
limit as x approaches-2 of-x^2+6x-8	\lim\:_{x\to\:-2}(-x^{2}+6x-8)
integral of aarctan(bx)	\int\:a\arctan(bx)dx
limit as x approaches 1 of x^2+4	\lim\:_{x\to\:1}(x^{2}+4)
tangent of y=-0.02x^2-0.6x+90	tangent\:y=-0.02x^{2}-0.6x+90
integral of 5ln(x)	\int\:5\ln(x)dx
derivative of 1/((x^2+1^3))	\frac{d}{dx}(\frac{1}{(x^{2}+1)^{3}})
integral of (e^{3x})/(e^{3x)+9}	\int\:\frac{e^{3x}}{e^{3x}+9}dx
integral from 0 to 1 of pi(6-3/2 x)^2	\int\:_{0}^{1}π(6-\frac{3}{2}x)^{2}dx
inverse oflaplace 2/(s^2+s)	inverselaplace\:\frac{2}{s^{2}+s}
y^{''}+9y=3cos(2x)+3	y^{\prime\:\prime\:}+9y=3\cos(2x)+3
integral of sqrt(9-x^2)(-2x)	\int\:\sqrt{9-x^{2}}(-2x)dx
derivative of (x-2^2(x+1))	\frac{d}{dx}((x-2)^{2}(x+1))
(\partial)/(\partial y)(x^2+y^2-9)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-9)
derivative of f(x)=6x^2+x-3	derivative\:f(x)=6x^{2}+x-3
laplacetransform t/2	laplacetransform\:\frac{t}{2}
area y=sqrt(x),x=9,y=0	area\:y=\sqrt{x},x=9,y=0
xy^'+2y=8x^2	xy^{\prime\:}+2y=8x^{2}
3y^{''}+5y^'+2y=0	3y^{\prime\:\prime\:}+5y^{\prime\:}+2y=0
integral of (3+2cos(x))^2	\int\:(3+2\cos(x))^{2}dx
limit as x approaches 2 of (6x)/(x-2)	\lim\:_{x\to\:2}(\frac{6x}{x-2})
tangent of f(x)=11sin(x),\at x=((3pi))/4	tangent\:f(x)=11\sin(x),\at\:x=\frac{(3π)}{4}
integral from 1 to 4 of ((2x+1))/(2x)	\int\:_{1}^{4}\frac{(2x+1)}{2x}dx
integral of sin(2x)(3-cos(2x))^2	\int\:\sin(2x)(3-\cos(2x))^{2}dx
limit as x approaches 2 of 1/(x^2-4x+4)	\lim\:_{x\to\:2}(\frac{1}{x^{2}-4x+4})
inverse oflaplace 5/s-5/s e^{-5s}	inverselaplace\:\frac{5}{s}-\frac{5}{s}e^{-5s}
sum from n=0 to infinity of-(-1)^{n+1}	\sum\:_{n=0}^{\infty\:}-(-1)^{n+1}
derivative of 3/(4x^2)	\frac{d}{dx}(\frac{3}{4x^{2}})
tangent of f(x)=x^4-13x^2+36	tangent\:f(x)=x^{4}-13x^{2}+36
integral from 0 to 1 of (45)/(x^5)	\int\:_{0}^{1}\frac{45}{x^{5}}dx
derivative of (1+4/x)^x	derivative\:(1+\frac{4}{x})^{x}
(\partial)/(\partial x)(2e^{x-2}-y)	\frac{\partial\:}{\partial\:x}(2e^{x-2}-y)
derivative of f(x)=(-x^2-1)/((x^2+1)^2)	derivative\:f(x)=\frac{-x^{2}-1}{(x^{2}+1)^{2}}
integral of sin(20x)sin(21x)	\int\:\sin(20x)\sin(21x)dx
integral of x(1/x)	\int\:x(\frac{1}{x})dx
derivative of (4x^2+5/(x^2+7))	\frac{d}{dx}(\frac{4x^{2}+5}{x^{2}+7})
(\partial)/(\partial y)(10-6y+e^{-3x})	\frac{\partial\:}{\partial\:y}(10-6y+e^{-3x})
d/(dt)(3e^t)	\frac{d}{dt}(3e^{t})
derivative of F(x)=(x^2)/(4+sqrt(x))	derivative\:F(x)=\frac{x^{2}}{4+\sqrt{x}}
(dy)/(dx)=y+y^3	\frac{dy}{dx}=y+y^{3}
integral from-9 to 4 of \|x+5\|	\int\:_{-9}^{4}\left\|x+5\right\|dx
integral of x/(sqrt(x^2-6x+8))	\int\:\frac{x}{\sqrt{x^{2}-6x+8}}dx
x^'=x^2,x(0)=1	x^{\prime\:}=x^{2},x(0)=1
sum from n=0 to infinity of (1/2)^{2n+1}	\sum\:_{n=0}^{\infty\:}(\frac{1}{2})^{2n+1}
derivative of 1/(x+1/x)	derivative\:\frac{1}{x+\frac{1}{x}}
limit as x approaches+(-0) of f(x)	\lim\:_{x\to\:+(-0)}(f(x))
derivative of cos(2x-sin(x))	\frac{d}{dx}(\cos(2x)-\sin(x))
integral from 1 to 16 of (x-7)/(sqrt(x))	\int\:_{1}^{16}\frac{x-7}{\sqrt{x}}dx
integral of 4/((1+2x)^3)	\int\:\frac{4}{(1+2x)^{3}}dx
integral from 1 to e^5 of (ln^3(x^2))/x	\int\:_{1}^{e^{5}}\frac{\ln^{3}(x^{2})}{x}dx
integral of x^{-1/4}sqrt(1+x^{1/4)}	\int\:x^{-\frac{1}{4}}\sqrt{1+x^{\frac{1}{4}}}dx
(\partial)/(\partial x)(5xcos(xy))	\frac{\partial\:}{\partial\:x}(5x\cos(xy))
(\partial)/(\partial x)(-hk^2+k^4)	\frac{\partial\:}{\partial\:x}(-hk^{2}+k^{4})

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