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Popular Calculus Problems

(\partial)/(\partial y)(x^5y^{10}cos(xy^2))	\frac{\partial\:}{\partial\:y}(x^{5}y^{10}\cos(xy^{2}))
derivative of \|2x-3\|	\frac{d}{dx}(\left\|2x-3\right\|)
derivative of 25e^{5x}	\frac{d}{dx}(25e^{5x})
(\partial)/(\partial x)((31xy)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{31xy}{x-y})
integral of sec^2(θ)tan^8(θ)	\int\:\sec^{2}(θ)\tan^{8}(θ)dθ
(\partial)/(\partial x)(1+y^2)	\frac{\partial\:}{\partial\:x}(1+y^{2})
9y^{''}-6y^'+y=0	9y^{\prime\:\prime\:}-6y^{\prime\:}+y=0
sum from n=1 to infinity of (1/7)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{7})^{n}
area 4x-x^2,x^2,2,0	area\:4x-x^{2},x^{2},2,0
limit as x approaches-6-of 1/((x+6)^6)	\lim\:_{x\to\:-6-}(\frac{1}{(x+6)^{6}})
f(x)=e^x+x	f(x)=e^{x}+x
(dy)/(dx)=(sqrt(1+cos(4x)))/(ye^{y^2)}	\frac{dy}{dx}=\frac{\sqrt{1+\cos(4x)}}{ye^{y^{2}}}
integral of (-1/(x^2))	\int\:(-\frac{1}{x^{2}})dx
tangent of f(x)=x^3+2,\at x=1	tangent\:f(x)=x^{3}+2,\at\:x=1
derivative of f(x)=sin^3(3x)	derivative\:f(x)=\sin^{3}(3x)
y^'+10y=4	y^{\prime\:}+10y=4
integral of 25sin^2(x)	\int\:25\sin^{2}(x)dx
tangent of 7x-7x	tangent\:7x-7x
limit as x approaches 9 of 1-4x^3	\lim\:_{x\to\:9}(1-4x^{3})
area 1/(20x^2),x, x/(20)	area\:\frac{1}{20x^{2}},x,\frac{x}{20}
integral of (x^3+2x^2-9x-6)/(x^2-9)	\int\:\frac{x^{3}+2x^{2}-9x-6}{x^{2}-9}dx
derivative of (x^2+1)/x	derivative\:\frac{x^{2}+1}{x}
tangent of f(x)= 5/x ,\at x=4	tangent\:f(x)=\frac{5}{x},\at\:x=4
limit as x approaches infinity of ln(x^{4/x})	\lim\:_{x\to\:\infty\:}(\ln(x^{\frac{4}{x}}))
integral of (x^3+2)/(x^2-1)	\int\:\frac{x^{3}+2}{x^{2}-1}dx
y^'-8/x y=(y^5)/(x^{11)}	y^{\prime\:}-\frac{8}{x}y=\frac{y^{5}}{x^{11}}
integral from 1 to 2 of (2x+x^2)	\int\:_{1}^{2}(2x+x^{2})dx
integral of (1/(1-x^2))	\int\:(\frac{1}{1-x^{2}})dx
xy^2(dy)/(dx)=y^3+x^3,y(1)=5	xy^{2}\frac{dy}{dx}=y^{3}+x^{3},y(1)=5
(\partial)/(\partial x)((2x)/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{2x}{x-y})
5t*(dy)/(dt)+2y=sqrt(t)	5t\cdot\:\frac{dy}{dt}+2y=\sqrt{t}
derivative of y^{3/2}(y+ce^y)	derivative\:y^{\frac{3}{2}}(y+ce^{y})
(\partial)/(\partial x)((ab)/(cx))	\frac{\partial\:}{\partial\:x}(\frac{a\cdot\:b}{c\cdot\:x})
derivative of (x^3+3^3)	\frac{d}{dx}((x^{3}+3)^{3})
integral of sin(x)(cos(x))^5	\int\:\sin(x)(\cos(x))^{5}dx
derivative of f(x)=5ln(4x)	derivative\:f(x)=5\ln(4x)
derivative of f(x)=(x-5)/((x+3)^4)	derivative\:f(x)=\frac{x-5}{(x+3)^{4}}
integral of sin(x)sec^{10}(x)	\int\:\sin(x)\sec^{10}(x)dx
derivative of 8/(t^8)-6/(t^6)+3/t	derivative\:\frac{8}{t^{8}}-\frac{6}{t^{6}}+\frac{3}{t}
derivative of f(x)=arctan(sin(4x))	derivative\:f(x)=\arctan(\sin(4x))
integral of 1/(sqrt(x^2+2x+82))	\int\:\frac{1}{\sqrt{x^{2}+2x+82}}dx
integral of (2sqrt(x)-3/(sqrt(x)))	\int\:(2\sqrt{x}-\frac{3}{\sqrt{x}})dx
integral from 1 to e^2 of x^5ln(x)	\int\:_{1}^{e^{2}}x^{5}\ln(x)dx
integral of xye^{xy^2}	\int\:xye^{xy^{2}}dy
derivative of (6x/(x^2-4))	\frac{d}{dx}(\frac{6x}{x^{2}-4})
integral from 0 to N of e^{-st}e^{-4t}	\int\:_{0}^{N}e^{-st}e^{-4t}dt
limit as x approaches+0+of (5x)/(sin(x))	\lim\:_{x\to\:+0+}(\frac{5x}{\sin(x)})
derivative of 1/(sqrt(x))*3e^x	derivative\:\frac{1}{\sqrt{x}}\cdot\:3e^{x}
integral of 1/(sqrt(9x^2-4))	\int\:\frac{1}{\sqrt{9x^{2}-4}}dx
integral of 1/(2x+x^3)	\int\:\frac{1}{2x+x^{3}}dx
integral of 1/(xsqrt(64x^4-1))	\int\:\frac{1}{x\sqrt{64x^{4}-1}}dx
derivative of 1/((x^3-2x^2+7^4))	\frac{d}{dx}(\frac{1}{(x^{3}-2x^{2}+7)^{4}})
derivative of \sqrt[5]{x}-2/x	\frac{d}{dx}(\sqrt[5]{x}-\frac{2}{x})
sum from n=1 to infinity of 4n-1	\sum\:_{n=1}^{\infty\:}4n-1
integral of 1/(1+3x^2)	\int\:\frac{1}{1+3x^{2}}dx
derivative of (3x/(squ(x,q)ar(x,q)esqrt(x^2+1)))	\frac{d}{dx}(\frac{3x}{squ(x,q)ar(x,q)e\sqrt{x^{2}+1}})
limit as x approaches 1 of 1/(x^3)	\lim\:_{x\to\:1}(\frac{1}{x^{3}})
integral of sin^3(2x)cos(2x)	\int\:\sin^{3}(2x)\cos(2x)dx
integral of 6/(sqrt(x^2+16))	\int\:\frac{6}{\sqrt{x^{2}+16}}dx
y^{''}-8y^'+15y=0,y(0)=1,y^'(0)=4	y^{\prime\:\prime\:}-8y^{\prime\:}+15y=0,y(0)=1,y^{\prime\:}(0)=4
(dy)/(dt)+y=2,y(0)=0	\frac{dy}{dt}+y=2,y(0)=0
integral of cos^4(θ)sin(θ)	\int\:\cos^{4}(θ)\sin(θ)dθ
derivative of ln(3x^2-2x)	\frac{d}{dx}(\ln(3x^{2}-2x))
derivative of ln((x^2+1^3))	\frac{d}{dx}(\ln((x^{2}+1)^{3}))
integral of (x+3)sqrt(4-x^2)	\int\:(x+3)\sqrt{4-x^{2}}dx
derivative of ln(15)	derivative\:\ln(15)
limit as x approaches 9 of ln(x-9)	\lim\:_{x\to\:9}(\ln(x-9))
derivative of ((x+1)/((x+2)))	\frac{d}{dx}(\frac{(x+1)}{(x+2)})
area x^2,4,[0,2]	area\:x^{2},4,[0,2]
integral from 0 to 4 of 1/(sqrt(16+t^2))	\int\:_{0}^{4}\frac{1}{\sqrt{16+t^{2}}}dt
derivative of sqrt(x^2+1/(x^2))	\frac{d}{dx}(\sqrt{x^{2}+\frac{1}{x^{2}}})
sum from n=0 to infinity of (7^n)/(6^n)	\sum\:_{n=0}^{\infty\:}\frac{7^{n}}{6^{n}}
integral of 8x(4x^2-3)^5	\int\:8x(4x^{2}-3)^{5}dx
integral of 1/((x+5)^2(x-1))	\int\:\frac{1}{(x+5)^{2}(x-1)}dx
integral of (x+1)/(x^2+4)	\int\:\frac{x+1}{x^{2}+4}dx
integral of x/(x^2+4x+13)	\int\:\frac{x}{x^{2}+4x+13}dx
tangent of sqrt(x-1)	tangent\:\sqrt{x-1}
derivative of 4x	derivative\:4x
limit as x approaches-3 of x^4-3x+10	\lim\:_{x\to\:-3}(x^{4}-3x+10)
derivative of G(t)=(1-4t)/(5+t)	derivative\:G(t)=\frac{1-4t}{5+t}
integral of 3/(8+3x)	\int\:\frac{3}{8+3x}dx
integral of sqrt(5-4x-4x^2)	\int\:\sqrt{5-4x-4x^{2}}dx
derivative of (-cos(2x)/2)	\frac{d}{dx}(\frac{-\cos(2x)}{2})
limit as x approaches-1+of 3/(x^2-1)	\lim\:_{x\to\:-1+}(\frac{3}{x^{2}-1})
integral from 0 to 1 of x(e^{-x^2})	\int\:_{0}^{1}x(e^{-x^{2}})dx
(\partial)/(\partial z)(x^{y^z})	\frac{\partial\:}{\partial\:z}(x^{y^{z}})
y^'=(-4y+44)^{1/2}	y^{\prime\:}=(-4y+44)^{\frac{1}{2}}
y^'-5y=(cos(x))*e^{5x}	y^{\prime\:}-5y=(\cos(x))\cdot\:e^{5x}
1/2 y^'+y=0	\frac{1}{2}y^{\prime\:}+y=0
derivative of sin(x-1)	\frac{d}{dx}(\sin(x-1))
integral of sqrt(cos(t))	\int\:\sqrt{\cos(t)}dt
integral of (-5x^6-3x^3-6x+5)	\int\:(-5x^{6}-3x^{3}-6x+5)dx
integral from-1 to 1 of (e^x)-(x^2-1)	\int\:_{-1}^{1}(e^{x})-(x^{2}-1)dx
2y^'+9y=3	2y^{\prime\:}+9y=3
integral from 1 to 2 of 7(ln(x))/(x^2)	\int\:_{1}^{2}7\frac{\ln(x)}{x^{2}}dx
integral of (e^{x^2})^2	\int\:(e^{x^{2}})^{2}dx
derivative of (3x+5^3)	\frac{d}{dx}((3x+5)^{3})
limit as x approaches 4 of 3x	\lim\:_{x\to\:4}(3x)
area x^2,0,4	area\:x^{2},0,4
derivative of cos((1-e^{5x})/(1+e^{5x)})	derivative\:\cos(\frac{1-e^{5x}}{1+e^{5x}})

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