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Popular Calculus Problems

derivative of f(x)=sin^2(tan(sqrt(x)))	derivative\:f(x)=\sin^{2}(\tan(\sqrt{x}))
d/(dt)(-1/(t+1))	\frac{d}{dt}(-\frac{1}{t+1})
derivative of f(x)= x/a	derivative\:f(x)=\frac{x}{a}
tangent of f(x)=x^2(4-x)^2,\at x=1	tangent\:f(x)=x^{2}(4-x)^{2},\at\:x=1
limit as x approaches infinity of sqrt((12x^3-4x+1)/(1+3x+2x^3))	\lim\:_{x\to\:\infty\:}(\sqrt{\frac{12x^{3}-4x+1}{1+3x+2x^{3}}})
integral from-3 to 3 of \|x\|-(x^2-6)	\int\:_{-3}^{3}\left\|x\right\|-(x^{2}-6)dx
integral from 5 to 6 of x/(x-5)	\int\:_{5}^{6}\frac{x}{x-5}dx
integral of (x^2)/(x+5)	\int\:\frac{x^{2}}{x+5}dx
integral of (x-3)/(x^3+3x^2+2x)	\int\:\frac{x-3}{x^{3}+3x^{2}+2x}dx
integral of e^{-(2r)/a}	\int\:e^{-\frac{2r}{a}}dr
derivative of 1/(1-4x)	\frac{d}{dx}(\frac{1}{1-4x})
derivative of (x^2/(3x-4))	\frac{d}{dx}(\frac{x^{2}}{3x-4})
integral of 2x^5	\int\:2x^{5}dx
limit as x approaches infinity of x_{1}	\lim\:_{x\to\:\infty\:}(x_{1})
derivative of f(x)=2x^e	derivative\:f(x)=2x^{e}
limit as x approaches 2+of 2-x^2	\lim\:_{x\to\:2+}(2-x^{2})
derivative of-6/(x^2)-5/x	derivative\:-\frac{6}{x^{2}}-\frac{5}{x}
limit as x approaches-2 of 1	\lim\:_{x\to\:-2}(1)
integral of x/(2y^4)	\int\:\frac{x}{2y^{4}}dx
integral from 0 to 2 of 4t	\int\:_{0}^{2}4tdt
integral of 3/(x^{3/4)}-4\sqrt[3]{x}+1	\int\:\frac{3}{x^{\frac{3}{4}}}-4\sqrt[3]{x}+1dx
integral of xsin^3(x)	\int\:x\sin^{3}(x)dx
derivative of x^3-4x	\frac{d}{dx}(x^{3}-4x)
(d^3)/(dx^3)(7/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{7}{x^{2}})
(\partial)/(\partial x)(a^x)	\frac{\partial\:}{\partial\:x}(a^{x})
integral of (5x)/((x^2+5)^2)	\int\:\frac{5x}{(x^{2}+5)^{2}}dx
tangent of (-6x)/((x^2+1))	tangent\:\frac{-6x}{(x^{2}+1)}
derivative of (sin^2(x)/(1+cos^2(x)))	\frac{d}{dx}(\frac{\sin^{2}(x)}{1+\cos^{2}(x)})
integral of 1/((4x+5)^2)	\int\:\frac{1}{(4x+5)^{2}}dx
tangent of f(x)=sqrt(7x+1),\at x=9	tangent\:f(x)=\sqrt{7x+1},\at\:x=9
integral of (2x+1)/(x^6+18x^4+81x^2)	\int\:\frac{2x+1}{x^{6}+18x^{4}+81x^{2}}dx
((log_{10}(x))/x)^'	(\frac{\log_{10}(x)}{x})^{\prime\:}
tangent of 6/(5x+3)	tangent\:\frac{6}{5x+3}
derivative of u(x)=2x	derivative\:u(x)=2x
integral of (x/(sqrt(x)))	\int\:(\frac{x}{\sqrt{x}})dx
(\partial)/(\partial x)((2x)^x)	\frac{\partial\:}{\partial\:x}((2x)^{x})
integral from 1 to 11 of 1/(x-7)	\int\:_{1}^{11}\frac{1}{x-7}dx
integral of 3x^2cos(x^3+2)	\int\:3x^{2}\cos(x^{3}+2)dx
derivative of 3x^2-7x+10	\frac{d}{dx}(3x^{2}-7x+10)
tangent of f(x)=2x^2+5x-3	tangent\:f(x)=2x^{2}+5x-3
integral of 1/((x^2-1)(x-3))	\int\:\frac{1}{(x^{2}-1)(x-3)}dx
integral of 2sqrt(x-2)	\int\:2\sqrt{x-2}dx
y^'+y/t =t^2y^4	y^{\prime\:}+\frac{y}{t}=t^{2}y^{4}
limit as x approaches+4+of 7/(x-4)	\lim\:_{x\to\:+4+}(\frac{7}{x-4})
integral of (x^6-x^3+16)/(x^4+4x^2)	\int\:\frac{x^{6}-x^{3}+16}{x^{4}+4x^{2}}dx
t(dy)/(dt)=t^3+15t^3y	t\frac{dy}{dt}=t^{3}+15t^{3}y
-6y^'+18x^2=0	-6y^{\prime\:}+18x^{2}=0
(t^3)dx+(xt^2+x^3)dt=0	(t^{3})dx+(xt^{2}+x^{3})dt=0
integral of cos(x)-cos^3(x)	\int\:\cos(x)-\cos^{3}(x)dx
derivative of-4x^{-3}	\frac{d}{dx}(-4x^{-3})
integral of 11x^{4/7}+7x^{-6/7}	\int\:11x^{\frac{4}{7}}+7x^{-\frac{6}{7}}dx
tangent of y=x^4	tangent\:y=x^{4}
limit as x approaches 0-of 1/(e^x+1)	\lim\:_{x\to\:0-}(\frac{1}{e^{x}+1})
derivative of (x^3/6-(3x^2)/2)	\frac{d}{dx}(\frac{x^{3}}{6}-\frac{3x^{2}}{2})
integral of sin^3(3x)sqrt(cos(3x))	\int\:\sin^{3}(3x)\sqrt{\cos(3x)}dx
integral of sec^2(x)csc^2(x)	\int\:\sec^{2}(x)\csc^{2}(x)dx
integral from 1/2 to 7 of 10xln(2x)	\int\:_{\frac{1}{2}}^{7}10x\ln(2x)dx
integral from 0 to 4 of 3e^{-x^2}	\int\:_{0}^{4}3e^{-x^{2}}dx
derivative of f(x)=9	derivative\:f(x)=9
integral of cot(m)xcsc^2(m)x	\int\:\cot(m)x\csc^{2}(m)xdx
tangent of f(x)=2x^3,\at x=-1	tangent\:f(x)=2x^{3},\at\:x=-1
tangent of ax^3,\at x=-5	tangent\:ax^{3},\at\:x=-5
derivative of y=3arctan(x-sqrt(1+x^2))	derivative\:y=3\arctan(x-\sqrt{1+x^{2}})
integral of (2x^3+10x^2-3x+4)	\int\:(2x^{3}+10x^{2}-3x+4)dx
y^{''}-6y^'=4t	y^{\prime\:\prime\:}-6y^{\prime\:}=4t
integral of (x-1)(x+2)(x+4)	\int\:(x-1)(x+2)(x+4)dx
(dy}{dx}=\frac{(y-sqrt(x^2+y^2)))/x	\frac{dy}{dx}=\frac{(y-\sqrt{x^{2}+y^{2}})}{x}
yy^'=(y^2-y)(2x+5)	yy^{\prime\:}=(y^{2}-y)(2x+5)
y^{''}+4y^'+5y=10	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=10
normal of f(x)=3sin(2x),\at x= pi/8	normal\:f(x)=3\sin(2x),\at\:x=\frac{π}{8}
derivative of y=(3x^2+3x-1)^4	derivative\:y=(3x^{2}+3x-1)^{4}
integral of (2sin(x)-5e^x)	\int\:(2\sin(x)-5e^{x})dx
integral of 1/2 sin(2θ)	\int\:\frac{1}{2}\sin(2θ)dθ
(\partial)/(\partial x)(x^2+2y^2-x^2y-1)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}-x^{2}y-1)
limit as x approaches-pi of (x+pi)csc(x)	\lim\:_{x\to\:-π}((x+π)\csc(x))
8t(dy)/(dt)+y=t^7	8t\frac{dy}{dt}+y=t^{7}
derivative of (x^2/(sqrt(x^4+x^2+1)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x^{4}+x^{2}+1}})
derivative of (2x/(x^2))	\frac{d}{dx}(\frac{2x}{x^{2}})
y^3-(10x+4)+3xy^2y^'=0	y^{3}-(10x+4)+3xy^{2}y^{\prime\:}=0
derivative of (3a+1)^2	derivative\:(3a+1)^{2}
integral from 1 to 9 of sqrt(x)ln(x)	\int\:_{1}^{9}\sqrt{x}\ln(x)dx
integral of (3x^5+1)/(3x-3x^5)	\int\:\frac{3x^{5}+1}{3x-3x^{5}}dx
derivative of ln(1-x^2)	derivative\:\ln(1-x^{2})
derivative of x^{-1/2}	derivative\:x^{-\frac{1}{2}}
area y=3-x,y=2x^2,[0,1]	area\:y=3-x,y=2x^{2},[0,1]
tangent of f(x)=2x^2+3x,(-2,2)	tangent\:f(x)=2x^{2}+3x,(-2,2)
(\partial)/(\partial x)(x^3-12x+y^3-27y)	\frac{\partial\:}{\partial\:x}(x^{3}-12x+y^{3}-27y)
(\partial)/(\partial x)(x*sin(2y))	\frac{\partial\:}{\partial\:x}(x\cdot\:\sin(2y))
d/(dy)(x^2-y)	\frac{d}{dy}(x^{2}-y)
integral of (x^2+x+3)/(x-2)	\int\:\frac{x^{2}+x+3}{x-2}dx
area y=x^2-2,y=((3x+1))/2	area\:y=x^{2}-2,y=\frac{(3x+1)}{2}
integral from 1 to 6 of 1/((6-x)^{2/3)}	\int\:_{1}^{6}\frac{1}{(6-x)^{\frac{2}{3}}}dx
integral of 3/2 (t+1)^{1/2}	\int\:\frac{3}{2}(t+1)^{\frac{1}{2}}dt
derivative of (x^3+7)/x	derivative\:\frac{x^{3}+7}{x}
integral of x^2*ln(2x-3)	\int\:x^{2}\cdot\:\ln(2x-3)dx
limit as x approaches pi of (1-cos(x))/x	\lim\:_{x\to\:π}(\frac{1-\cos(x)}{x})
derivative of (2x/(x^2+81))	\frac{d}{dx}(\frac{2x}{x^{2}+81})
slope of (1,4),(-1,-4)	slope\:(1,4),(-1,-4)
integral of sin(x)sin(x+pi/6)	\int\:\sin(x)\sin(x+\frac{π}{6})dx
(\partial)/(\partial x)(6x^2cos(y^7))	\frac{\partial\:}{\partial\:x}(6x^{2}\cos(y^{7}))

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