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Popular Calculus Problems

derivative of (11x^4+5^3)	\frac{d}{dx}((11x^{4}+5)^{3})
integral of xsec^2(9x)	\int\:x\sec^{2}(9x)dx
(\partial)/(\partial y)(xcos(x+y))	\frac{\partial\:}{\partial\:y}(x\cos(x+y))
(dy)/(dx)+2y=20e^{3x}	\frac{dy}{dx}+2y=20e^{3x}
(\partial)/(\partial y)((7y)/(x^4))	\frac{\partial\:}{\partial\:y}(\frac{7y}{x^{4}})
limit as x approaches 1 of 2x-5	\lim\:_{x\to\:1}(2x-5)
derivative of 1/8 x^2	\frac{d}{dx}(\frac{1}{8}x^{2})
(\partial)/(\partial x)(-y^2sin(xy^2))	\frac{\partial\:}{\partial\:x}(-y^{2}\sin(xy^{2}))
integral of 3/(3sin(x)-4cos(x))	\int\:\frac{3}{3\sin(x)-4\cos(x)}dx
derivative of 1/(cot(1/t))	derivative\:\frac{1}{\cot(\frac{1}{t})}
derivative of 3^{cos(2x})	\frac{d}{dx}(3^{\cos(2x)})
limit as x approaches 3 of (10)/(x^2)	\lim\:_{x\to\:3}(\frac{10}{x^{2}})
integral from 0 to 4 of ((5x)/(x^2+9))	\int\:_{0}^{4}(\frac{5x}{x^{2}+9})dx
derivative of (2x+sqrt(x)(x^2-x))	\frac{d}{dx}((2x+\sqrt{x})(x^{2}-x))
derivative of sec^2(θ)	derivative\:\sec^{2}(θ)
derivative of (cos(x)/(x^6))	\frac{d}{dx}(\frac{\cos(x)}{x^{6}})
taylor 1/(2-x)	taylor\:\frac{1}{2-x}
integral of (1+x+e^x)	\int\:(1+x+e^{x})dx
f(z)=tan(e^{-6z})	f(z)=\tan(e^{-6z})
derivative of sin^4(2x+3)	\frac{d}{dx}(\sin^{4}(2x+3))
derivative of (1/x)^3	derivative\:(\frac{1}{x})^{3}
tangent of f(x)=(3x-1)/(x^2+1),\at x=6	tangent\:f(x)=\frac{3x-1}{x^{2}+1},\at\:x=6
integral from 1 to 2 of (4x^2-7x-12)/(x(x+2)(x-3))	\int\:_{1}^{2}\frac{4x^{2}-7x-12}{x(x+2)(x-3)}dx
derivative of y=ln(x^2+5)	derivative\:y=\ln(x^{2}+5)
integral of (sin(2x)+cos(2x))	\int\:(\sin(2x)+\cos(2x))dx
area y=x^2,y=2x-x^2	area\:y=x^{2},y=2x-x^{2}
derivative of (qx+r(q,x,t)/(sx+t))	\frac{d}{dx}(\frac{qx+r(q,x,t)}{sx+t})
integral of (x+4)sqrt(6-x)	\int\:(x+4)\sqrt{6-x}dx
integral of (2x^3)/(sqrt(x^2-4))	\int\:\frac{2x^{3}}{\sqrt{x^{2}-4}}dx
derivative of 3x^3+2x+9	\frac{d}{dx}(3x^{3}+2x+9)
limit as x approaches 0+of (csc(x))^x	\lim\:_{x\to\:0+}((\csc(x))^{x})
derivative of x^2+6x+3	derivative\:x^{2}+6x+3
derivative of \sqrt[3]{(1+x^3/(1-x^3)})	\frac{d}{dx}(\sqrt[3]{\frac{1+x^{3}}{1-x^{3}}})
limit as x approaches 8+of ln(x^2-64)	\lim\:_{x\to\:8+}(\ln(x^{2}-64))
taylor 1/(1-x),1.1	taylor\:\frac{1}{1-x},1.1
inverse oflaplace 3/((s+2)*(4s^2+4s+5))	inverselaplace\:\frac{3}{(s+2)\cdot\:(4s^{2}+4s+5)}
derivative of x^4-3x^3+2x^2	\frac{d}{dx}(x^{4}-3x^{3}+2x^{2})
limit as x approaches infinity of (3x+5)/(6x-8)	\lim\:_{x\to\:\infty\:}(\frac{3x+5}{6x-8})
derivative of sin^{2/3}(x)	\frac{d}{dx}(\sin^{\frac{2}{3}}(x))
derivative of 4sin(x+4xcos(x))	\frac{d}{dx}(4\sin(x)+4x\cos(x))
(\partial)/(\partial x)(ln(x+5y+8z))	\frac{\partial\:}{\partial\:x}(\ln(x+5y+8z))
limit as t approaches-3 of e^t	\lim\:_{t\to\:-3}(e^{t})
(\partial)/(\partial y)(x/(x^4-y^3))	\frac{\partial\:}{\partial\:y}(\frac{x}{x^{4}-y^{3}})
limit as x approaches-1 of 2x^3+x+7	\lim\:_{x\to\:-1}(2x^{3}+x+7)
limit as x approaches 1+of 2x+4	\lim\:_{x\to\:1+}(2x+4)
inverse oflaplace {(10s)/(s^2+16)}	inverselaplace\:\left\{\frac{10s}{s^{2}+16}\right\}
derivative of (4x/5)	\frac{d}{dx}(\frac{4x}{5})
f^'(x)=12x^3-63x^2-72x+4	f^{\prime\:}(x)=12x^{3}-63x^{2}-72x+4
derivative of y=(f(x))/(x^6)	derivative\:y=\frac{f(x)}{x^{6}}
integral from 0 to 1 of x-x^k	\int\:_{0}^{1}x-x^{k}dx
derivative of 3	derivative\:3
derivative of arctan(x/(2000))	\frac{d}{dx}(\arctan(\frac{x}{2000}))
integral of sqrt(x)*(e^{sqrt(x)})/(2x)	\int\:\sqrt{x}\cdot\:\frac{e^{\sqrt{x}}}{2x}dx
derivative of xe^{3{z}(x})	\frac{d}{dx}(xe^{3{z}(x)})
tangent of f(x)=x^3+2/x ,\at x=1	tangent\:f(x)=x^{3}+\frac{2}{x},\at\:x=1
laplacetransform \delta(t)	laplacetransform\:\delta(t)
y^'-2y=5	y^{\prime\:}-2y=5
integral of (ln(sqrt(6x)))/x	\int\:\frac{\ln(\sqrt{6x})}{x}dx
derivative of 5x^7	\frac{d}{dx}(5x^{7})
integral from 0 to pi of cos(x)sin(nx)	\int\:_{0}^{π}\cos(x)\sin(nx)dx
limit as x approaches 3 of x^2+1	\lim\:_{x\to\:3}(x^{2}+1)
integral of-t/2	\int\:-\frac{t}{2}dt
integral from 0 to 4 of-x^2+4x	\int\:_{0}^{4}-x^{2}+4xdx
derivative of (7x^2-1/x)	\frac{d}{dx}(\frac{7x^{2}-1}{x})
y^{''}+4y=0,y(0)=1,y^'(0)=4	y^{\prime\:\prime\:}+4y=0,y(0)=1,y^{\prime\:}(0)=4
(dy)/(dx)=32x^3y^3,y(0)=k	\frac{dy}{dx}=32x^{3}y^{3},y(0)=k
integral of [(a^3)/(x^2+a^2)]^2	\int\:[\frac{a^{3}}{x^{2}+a^{2}}]^{2}dx
sum from n=1 to infinity of (n/(n+4))^n	\sum\:_{n=1}^{\infty\:}(\frac{n}{n+4})^{n}
integral of cos(4x-3)	\int\:\cos(4x-3)dx
area y=3x-x^2,y=-3x	area\:y=3x-x^{2},y=-3x
slope of (2/7 ,5),(10,39)	slope\:(\frac{2}{7},5),(10,39)
integral from 15 to 35 of (x^2x)	\int\:_{15}^{35}(x^{2}x)dx
(\partial)/(\partial y)(x/y-yz)	\frac{\partial\:}{\partial\:y}(\frac{x}{y}-yz)
integral of (3x-1)/(x^{2/3)}	\int\:\frac{3x-1}{x^{\frac{2}{3}}}dx
derivative of 1/(3x^2+1)	\frac{d}{dx}(\frac{1}{3x^{2}+1})
integral of x^2e^{4x^3}	\int\:x^{2}e^{4x^{3}}dx
derivative of 3sin(4x)	derivative\:3\sin(4x)
derivative of x^4+cos(x+1)	\frac{d}{dx}(x^{4}+\cos(x)+1)
integral of ((16-9x^2)^{3/2})/(x^6)	\int\:\frac{(16-9x^{2})^{\frac{3}{2}}}{x^{6}}dx
sum from n=1 to infinity of (((3n-1))/((3n)))^{n^2}	\sum\:_{n=1}^{\infty\:}(\frac{(3n-1)}{(3n)})^{n^{2}}
tan(x)sin^2(y)dx+cos^2(x)cot(y)dy=0	\tan(x)\sin^{2}(y)dx+\cos^{2}(x)\cot(y)dy=0
sum from n=0 to infinity of 1+1/(n^2)	\sum\:_{n=0}^{\infty\:}1+\frac{1}{n^{2}}
integral from-2 to 2 of x^2e^{x^3+8}	\int\:_{-2}^{2}x^{2}e^{x^{3}+8}dx
derivative of 5ln(x)	derivative\:5\ln(x)
derivative of x^2log_{3}(x^3)	derivative\:x^{2}\log_{3}(x^{3})
integral of (8x-7/x)	\int\:(8x-\frac{7}{x})dx
tangent of y=cos(x),\at x=(3pi)/2	tangent\:y=\cos(x),\at\:x=\frac{3π}{2}
derivative of f(x)= 5/((2x-3)^4)	derivative\:f(x)=\frac{5}{(2x-3)^{4}}
derivative of sin(xln(5x))	\frac{d}{dx}(\sin(x)\ln(5x))
derivative of e^{19}	derivative\:e^{19}
(dy)/(dx)=e^4x+7y	\frac{dy}{dx}=e^{4}x+7y
integral of xsqrt(3x^2-6)	\int\:x\sqrt{3x^{2}-6}dx
limit as x approaches 2 of (2x^2-5x+2)/(x^3-2x^2)	\lim\:_{x\to\:2}(\frac{2x^{2}-5x+2}{x^{3}-2x^{2}})
derivative of ax^2e^{-3x}	\frac{d}{dx}(ax^{2}e^{-3x})
(\partial)/(\partial x)(x^4-8xy-5y^2)	\frac{\partial\:}{\partial\:x}(x^{4}-8xy-5y^{2})
integral of 5/(\sqrt[4]{x^2)}	\int\:\frac{5}{\sqrt[4]{x^{2}}}dx
(\partial)/(\partial x)(ln(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{2}+z^{2}))
limit as x approaches 2 of (11x)/(4-x^2)	\lim\:_{x\to\:2}(\frac{11x}{4-x^{2}})
derivative of (3x-5)(x^2+4)	derivative\:(3x-5)(x^{2}+4)
integral of (7x+14)/(x^2+5x-6)	\int\:\frac{7x+14}{x^{2}+5x-6}dx

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