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Popular Calculus Problems

(\partial)/(\partial x)(y^2ln(y)-2xy^2)	\frac{\partial\:}{\partial\:x}(y^{2}\ln(y)-2xy^{2})
derivative of (x^2-9x+20/((x+2)(x-2)))	\frac{d}{dx}(\frac{x^{2}-9x+20}{(x+2)(x-2)})
derivative of (log_{10}(x)^{sinh(x)})	\frac{d}{dx}((\log_{10}(x))^{\sinh(x)})
tangent of f(x)=x^2-4,\at a=1	tangent\:f(x)=x^{2}-4,\at\:a=1
integral from 5 to 9 of (sqrt(9-y)+2)^2	\int\:_{5}^{9}(\sqrt{9-y}+2)^{2}dy
limit as x approaches 2 of 1/2 x+c	\lim\:_{x\to\:2}(\frac{1}{2}x+c)
derivative of (x+2/(3x-4))	\frac{d}{dx}(\frac{x+2}{3x-4})
sum from n=1 to infinity of 8*(1/5)^n	\sum\:_{n=1}^{\infty\:}8\cdot\:(\frac{1}{5})^{n}
integral of (7x+1)/(x(x^2-1))	\int\:\frac{7x+1}{x(x^{2}-1)}dx
integral from 0 to 3 of 1/(sqrt(1+x))	\int\:_{0}^{3}\frac{1}{\sqrt{1+x}}dx
integral of (z^2)/(1^3)+z^3	\int\:\frac{z^{2}}{1^{3}}+z^{3}
integral of 20x^3-12x^2+6x	\int\:20x^{3}-12x^{2}+6xdx
sum from n=1 to infinity of 7/(n^2+9)	\sum\:_{n=1}^{\infty\:}\frac{7}{n^{2}+9}
limit as x approaches 0+of (e^x)/(e^x-1)	\lim\:_{x\to\:0+}(\frac{e^{x}}{e^{x}-1})
(\partial)/(\partial y)(e^{y^2}-e^y)	\frac{\partial\:}{\partial\:y}(e^{y^{2}}-e^{y})
derivative of f(r)= 4/3 pir^3	derivative\:f(r)=\frac{4}{3}πr^{3}
integral of 3y^2z+ye^x	\int\:3y^{2}z+ye^{x}dx
integral of t(t-1)^{12}	\int\:t(t-1)^{12}dt
(\partial)/(\partial x)(sin(5x-2y))	\frac{\partial\:}{\partial\:x}(\sin(5x-2y))
(\partial)/(\partial x)(2ye^{4x^2-6y})	\frac{\partial\:}{\partial\:x}(2ye^{4x^{2}-6y})
derivative of f(x)=-x	derivative\:f(x)=-x
limit as x approaches infinity of-3,x	\lim\:_{x\to\:\infty\:}(-3,x)
derivative of (x+1^2e^x)	\frac{d}{dx}((x+1)^{2}e^{x})
limit as x approaches 9 of \sqrt[4]{9-x}	\lim\:_{x\to\:9}(\sqrt[4]{9-x})
limit as x approaches (9pi)/2 of sec(x)	\lim\:_{x\to\:\frac{9π}{2}}(\sec(x))
derivative of ln(1/(x^3+3))	\frac{d}{dx}(\ln(\frac{1}{x^{3}+3}))
4y^2ydx+xydy=0	4y^{2}ydx+xydy=0
(\partial)/(\partial x)(ln(9ye^{xy}))	\frac{\partial\:}{\partial\:x}(\ln(9ye^{xy}))
derivative of 1/(3x^3)	derivative\:\frac{1}{3x^{3}}
integral of ((24x)/(3-4x^2))	\int\:(\frac{24x}{3-4x^{2}})dx
derivative of 2(cos(x/2-(sqrt(2))/2))	\frac{d}{dx}(2(\cos(\frac{x}{2})-\frac{\sqrt{2}}{2}))
derivative of f(x)=\sqrt[3]{1+4x}	derivative\:f(x)=\sqrt[3]{1+4x}
integral from 2 to 3 of 4e^{4x}	\int\:_{2}^{3}4e^{4x}dx
y^'+3y=te^{4t}	y^{\prime\:}+3y=te^{4t}
integral from 16 to 25 of (sqrt(x-16))/x	\int\:_{16}^{25}\frac{\sqrt{x-16}}{x}dx
integral of cos(x)(8+5sin^2(x))	\int\:\cos(x)(8+5\sin^{2}(x))dx
integral of 1/(x^2+6x+8)	\int\:\frac{1}{x^{2}+6x+8}dx
integral of 2x-x^2	\int\:2x-x^{2}dx
(\partial)/(\partial x)(sin(pi(6x-2y)))	\frac{\partial\:}{\partial\:x}(\sin(π(6x-2y)))
integral from 1 to infinity of 1/(x^2+2)	\int\:_{1}^{\infty\:}\frac{1}{x^{2}+2}dx
limit as x approaches-6 of x^2-7	\lim\:_{x\to\:-6}(x^{2}-7)
integral of (x-240)/(200)	\int\:\frac{x-240}{200}dx
sum from n=1 to infinity of 7/(n^2+25)	\sum\:_{n=1}^{\infty\:}\frac{7}{n^{2}+25}
integral from 0 to 1/2 of 5/(1+4x^2)	\int\:_{0}^{\frac{1}{2}}\frac{5}{1+4x^{2}}dx
derivative of e^x(3x^2-x+1)	derivative\:e^{x}(3x^{2}-x+1)
(\partial)/(\partial y)(e^{-xy^2}+y^3x^4)	\frac{\partial\:}{\partial\:y}(e^{-xy^{2}}+y^{3}x^{4})
roots xsqrt(y)	roots\:x\sqrt{y}
sum from n=1 to infinity of n^3+n	\sum\:_{n=1}^{\infty\:}n^{3}+n
(x^5)^'	(x^{5})^{\prime\:}
integral of 1/(4x+9)	\int\:\frac{1}{4x+9}dx
taylor x/(1+3x^2)	taylor\:\frac{x}{1+3x^{2}}
integral from 0 to pi of (pi-x)sin(nx)	\int\:_{0}^{π}(π-x)\sin(nx)dx
(\partial)/(\partial x)(xy^2-x^3y)	\frac{\partial\:}{\partial\:x}(xy^{2}-x^{3}y)
laplacetransform 4cos(4t)	laplacetransform\:4\cos(4t)
derivative of f(x)=(2x^3+3)^6	derivative\:f(x)=(2x^{3}+3)^{6}
limit as x approaches infinity of \sqrt[x]{4^x+9^x}	\lim\:_{x\to\:\infty\:}(\sqrt[x]{4^{x}+9^{x}})
derivative of (cos(x)/(sqrt(2)))	\frac{d}{dx}(\frac{\cos(x)}{\sqrt{2}})
tangent of-2x^2	tangent\:-2x^{2}
integral of 9x^2-8x	\int\:9x^{2}-8xdx
integral of 3/(sqrt(1+9x^2))	\int\:\frac{3}{\sqrt{1+9x^{2}}}dx
integral of (sqrt(y^2-4))/y	\int\:\frac{\sqrt{y^{2}-4}}{y}dy
derivative of (x^5-8x^3+x+6/x)	\frac{d}{dx}(\frac{x^{5}-8x^{3}+x+6}{x})
limit as x approaches 0 of 2x^3-4x+2	\lim\:_{x\to\:0}(2x^{3}-4x+2)
integral of (2/x+3sin(x)-4e^x)	\int\:(\frac{2}{x}+3\sin(x)-4e^{x})dx
area y=sqrt(1+3x),1<= x<= 9	area\:y=\sqrt{1+3x},1\le\:x\le\:9
limit as x approaches infinity of a^x	\lim\:_{x\to\:\infty\:}(a^{x})
derivative of 5x^5ln(x)	\frac{d}{dx}(5x^{5}\ln(x))
integral from 3 to 4 of (2x-3)/6	\int\:_{3}^{4}\frac{2x-3}{6}dx
integral from 2 to 3 of (3-x)	\int\:_{2}^{3}(3-x)dx
integral of p^5ln(p)	\int\:p^{5}\ln(p)dp
(dy)/(dx)=(xy+2)/(x+1)	\frac{dy}{dx}=\frac{xy+2}{x+1}
d/(dt)(t-cos(t))	\frac{d}{dt}(t-\cos(t))
limit as x approaches+2 of xsqrt(13-x^2)	\lim\:_{x\to\:+2}(x\sqrt{13-x^{2}})
integral of 1+2/x	\int\:1+\frac{2}{x}dx
derivative of cos(sin(5x^2))	\frac{d}{dx}(\cos(\sin(5x^{2})))
derivative of (x^3-1/(x^3+1))	\frac{d}{dx}(\frac{x^{3}-1}{x^{3}+1})
y^{''}+y=cos(t)	y^{\prime\:\prime\:}+y=\cos(t)
tangent of f(x)=x^3-3x^2+2x-2,\at x=2	tangent\:f(x)=x^{3}-3x^{2}+2x-2,\at\:x=2
integral of 2x^2+2x	\int\:2x^{2}+2xdx
integral of e^{-0.5t}	\int\:e^{-0.5t}dt
(\partial)/(\partial x)(22cos(x))	\frac{\partial\:}{\partial\:x}(22\cos(x))
(\partial)/(\partial y)(y/x)	\frac{\partial\:}{\partial\:y}(\frac{y}{x})
integral of-25cos(x)	\int\:-25\cos(x)dx
inverse oflaplace 9/(s^3+9s^2+9s)	inverselaplace\:\frac{9}{s^{3}+9s^{2}+9s}
derivative of ((x^3)/3-((x^2))/2-2x-1)	\frac{d}{dx}(\frac{(x^{3})}{3}-\frac{(x^{2})}{2}-2x-1)
integral of 100sin(500x)	\int\:100\sin(500x)dx
1/(8x)(dy)/(dx)=ysqrt(4x^2-1)	\frac{1}{8x}\frac{dy}{dx}=y\sqrt{4x^{2}-1}
integral of 5-0.04x+3x^2	\int\:5-0.04x+3x^{2}dx
derivative of (2x/(x^2-36))	\frac{d}{dx}(\frac{2x}{x^{2}-36})
4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9	4y^{\prime\:\prime\:}-4y^{\prime\:}-3y=0,y(0)=1,y^{\prime\:}(0)=9
limit as x approaches-pi of csc(x)	\lim\:_{x\to\:-π}(\csc(x))
(\partial)/(\partial x)((e^x+e^y)^6)	\frac{\partial\:}{\partial\:x}((e^{x}+e^{y})^{6})
integral of (sqrt(1-x^2))/((x^2-1)^2)	\int\:\frac{\sqrt{1-x^{2}}}{(x^{2}-1)^{2}}dx
limit as x approaches 2 of x^2-3x	\lim\:_{x\to\:2}(x^{2}-3x)
y^{''}+2y^'=2x+7-e-2x	y^{\prime\:\prime\:}+2y^{\prime\:}=2x+7-e-2x
integral of sin(2x)cos^4(2x)	\int\:\sin(2x)\cos^{4}(2x)dx
derivative of f(x)=(7x+6)^2	derivative\:f(x)=(7x+6)^{2}
derivative of (-16x^2+1)^2	derivative\:(-16x^{2}+1)^{2}
y^{''}=sin(x)	y^{\prime\:\prime\:}=\sin(x)
x((dy}{dx})-y=(\frac{x^3)/y)e^{y/x}	x(\frac{dy}{dx})-y=(\frac{x^{3}}{y})e^{\frac{y}{x}}

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