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Popular Calculus Problems

(\partial)/(\partial x)((x+y)^3)	\frac{\partial\:}{\partial\:x}((x+y)^{3})
(\partial)/(\partial x)(x^2yz-xyz^3)	\frac{\partial\:}{\partial\:x}(x^{2}yz-xyz^{3})
area y=7x,y=x^2-8	area\:y=7x,y=x^{2}-8
derivative of f(x)=sqrt(x/(x+9))	derivative\:f(x)=\sqrt{\frac{x}{x+9}}
derivative of 2e^x-2	\frac{d}{dx}(2e^{x}-2)
derivative of (2x+3(2x-3))	\frac{d}{dx}((2x+3)(2x-3))
derivative of-x^2+3x	\frac{d}{dx}(-x^{2}+3x)
limit as x approaches infinity of 1/(x^{4/3)}	\lim\:_{x\to\:\infty\:}(\frac{1}{x^{\frac{4}{3}}})
(x^2+1)dy+(4xy-x^2)dx=0	(x^{2}+1)dy+(4xy-x^{2})dx=0
d/(dy)(x/(y^2+x^2))	\frac{d}{dy}(\frac{x}{y^{2}+x^{2}})
integral of 4x(2x^2+1)8	\int\:4x(2x^{2}+1)8dx
(dy)/(dt)-(3/t)y=2t^3e^{(2t)}	\frac{dy}{dt}-(\frac{3}{t})\cdot\:y=2t^{3}\cdot\:e^{(2t)}
d/(dt)(5e^{-2t}+3te^{-2t}-2)	\frac{d}{dt}(5e^{-2t}+3te^{-2t}-2)
y^{''}-4y^'-5y=0,y(1)=0,y^'(1)=4	y^{\prime\:\prime\:}-4y^{\prime\:}-5y=0,y(1)=0,y^{\prime\:}(1)=4
taylor xcos(x)	taylor\:x\cos(x)
integral of (2+x)/(4x^2-4x-3)	\int\:\frac{2+x}{4x^{2}-4x-3}dx
derivative of f(x)=ln(x-1)	derivative\:f(x)=\ln(x-1)
integral of (12x^2-8x+2)	\int\:(12x^{2}-8x+2)dx
(dy}{dx}=\frac{(x-1))/y	\frac{dy}{dx}=\frac{(x-1)}{y}
derivative of 7arcsin(x^2)	\frac{d}{dx}(7\arcsin(x^{2}))
area y=1x,(0,4)	area\:y=1x,(0,4)
t(dy)/(dt)+9y= 1/t	t\frac{dy}{dt}+9y=\frac{1}{t}
integral of (sqrt(2y^2-3))/(y^2)	\int\:\frac{\sqrt{2y^{2}-3}}{y^{2}}dy
derivative of (2x^{4x})	\frac{d}{dx}((2x)^{4x})
integral of (x^2+5)	\int\:(x^{2}+5)dx
derivative of (cos(ln(x)))/x	derivative\:\frac{\cos(\ln(x))}{x}
integral of (sqrt(x+1))/x	\int\:\frac{\sqrt{x+1}}{x}dx
y^'=4y^2+1	y^{\prime\:}=4y^{2}+1
integral of cos(k)x	\int\:\cos(k)xdx
derivative of 5ln(\sqrt[5]{e^{x^3}})	\frac{d}{dx}(5\ln(\sqrt[5]{e^{x^{3}}}))
integral of (x^2+2x)cos(x^3+3x^2-47)	\int\:(x^{2}+2x)\cos(x^{3}+3x^{2}-47)dx
derivative of (7x+8)(8x-9)	derivative\:(7x+8)(8x-9)
derivative of y=(sqrt(x))/(4+x)	derivative\:y=\frac{\sqrt{x}}{4+x}
sum from n=1 to infinity of 4/(n(n+3)!)	\sum\:_{n=1}^{\infty\:}\frac{4}{n(n+3)!}
integral of 3x^2y	\int\:3x^{2}ydx
derivative of sqrt((x^2+1/(x^2+4)))	\frac{d}{dx}(\sqrt{\frac{x^{2}+1}{x^{2}+4}})
derivative of 6\sqrt[3]{x}	derivative\:6\sqrt[3]{x}
(\partial)/(\partial x)(2x^4y+sin(x^4))	\frac{\partial\:}{\partial\:x}(2x^{4}y+\sin(x^{4}))
integral of (arcsin(ln(x)))/x	\int\:\frac{\arcsin(\ln(x))}{x}dx
derivative of 1/(cos(x/2))	derivative\:\frac{1}{\cos(\frac{x}{2})}
derivative of-(2(-3x^2-1)/((x^2-1)^3))	\frac{d}{dx}(-\frac{2(-3x^{2}-1)}{(x^{2}-1)^{3}})
derivative of (x-5)(x+4)(x+6)	derivative\:(x-5)(x+4)(x+6)
derivative of ((x+2(x+1))/(2x-1))	\frac{d}{dx}(\frac{(x+2)(x+1)}{2x-1})
area y=4x^2,y=2\sqrt[3]{2}	area\:y=4x^{2},y=2\sqrt[3]{2}
derivative of f(x)=ln(15)	derivative\:f(x)=\ln(15)
integral of 1/(csc(y))	\int\:\frac{1}{\csc(y)}dy
integral from 0 to infinity of u^2e^{-u}	\int\:_{0}^{\infty\:}u^{2}e^{-u}du
(\partial)/(\partial y)(z-sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:y}(z-\sqrt{x^{2}+y^{2}})
integral of 5x^2+3	\int\:5x^{2}+3dx
derivative of-3e^{x^5}	derivative\:-3e^{x^{5}}
(\partial)/(\partial x)((5y)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{5y}{x^{2}+y^{2}})
integral of ((x-1))/((x+1))	\int\:\frac{(x-1)}{(x+1)}dx
integral of e^{-tx}	\int\:e^{-tx}dx
integral of 2/(sqrt(25-2x^2))	\int\:\frac{2}{\sqrt{25-2x^{2}}}dx
derivative of 6x+4/x	derivative\:6x+\frac{4}{x}
sum from n=1 to infinity of 1/(n(ln(n)))	\sum\:_{n=1}^{\infty\:}\frac{1}{n(\ln(n))}
derivative of xcos(x)sin(x)	derivative\:x\cos(x)\sin(x)
integral of-2/(1-2x)	\int\:-\frac{2}{1-2x}dx
integral from 1 to 4 of (x^2+1)/(5x-x^2)	\int\:_{1}^{4}\frac{x^{2}+1}{5x-x^{2}}dx
implicit (dy}{dx},\frac{(x^2))/4+y^2=1	implicit\:\frac{dy}{dx},\frac{(x^{2})}{4}+y^{2}=1
derivative of 1/(4x^3)	\frac{d}{dx}(\frac{1}{4x^{3}})
derivative of ln(x^3-1)	\frac{d}{dx}(\ln(x^{3}-1))
integral from-4 to 2 of (12-x-x^2)-(x+4)	\int\:_{-4}^{2}(12-x-x^{2})-(x+4)dx
(\partial)/(\partial x)(x^5+7x^5y)	\frac{\partial\:}{\partial\:x}(x^{5}+7x^{5}y)
limit as x approaches-4 of (x^2+3)/(x-1)	\lim\:_{x\to\:-4}(\frac{x^{2}+3}{x-1})
e^yy^'+t/(y+1)= 2/(y+1)	e^{y}y^{\prime\:}+\frac{t}{y+1}=\frac{2}{y+1}
limit as x approaches infinity of 1/(6^{x+1)}	\lim\:_{x\to\:\infty\:}(\frac{1}{6^{x+1}})
slope of (6,2),(-3,5)	slope\:(6,2),(-3,5)
derivative of (2x-3)/(4x+1)	derivative\:\frac{2x-3}{4x+1}
integral of (3x-1)sqrt(x+6)	\int\:(3x-1)\sqrt{x+6}dx
derivative of ln(sqrt((2x+1)/(x^2-4)))	derivative\:\ln(\sqrt{\frac{2x+1}{x^{2}-4}})
inverse oflaplace 1/(s^2(s^2+1)^2)	inverselaplace\:\frac{1}{s^{2}(s^{2}+1)^{2}}
area y=e^x,y=e^{2x},x=ln(2),x=ln(3)	area\:y=e^{x},y=e^{2x},x=\ln(2),x=\ln(3)
limit as x approaches 0+of (1+4x)^{cot(x)}	\lim\:_{x\to\:0+}((1+4x)^{\cot(x)})
taylor sqrt(x^2+1)	taylor\:\sqrt{x^{2}+1}
y^'=sqrt(2y+39)	y^{\prime\:}=\sqrt{2y+39}
derivative of (x^{3/5}sqrt(x^3+2x-6)/((4x-3)^8))	\frac{d}{dx}(\frac{x^{\frac{3}{5}}\sqrt{x^{3}+2x-6}}{(4x-3)^{8}})
derivative of f(x)= 4/(x-2)	derivative\:f(x)=\frac{4}{x-2}
limit as x approaches 4-of e^{3/(4-x)}	\lim\:_{x\to\:4-}(e^{\frac{3}{4-x}})
integral of x^5(x-9)	\int\:x^{5}(x-9)dx
inverse oflaplace (40s+20)/(s^2+9s+14)	inverselaplace\:\frac{40s+20}{s^{2}+9s+14}
(\partial)/(\partial x)(x-a)	\frac{\partial\:}{\partial\:x}(x-a)
integral of (3sin(t)-2cos(t))	\int\:(3\sin(t)-2\cos(t))dt
integral of sqrt((9-x^2)/(x^2))	\int\:\sqrt{\frac{9-x^{2}}{x^{2}}}dx
(\partial)/(\partial x)(blog_{10}(x))	\frac{\partial\:}{\partial\:x}(b\log_{10}(x))
(\partial)/(\partial x)((x_{1}+x_{2})^2)	\frac{\partial\:}{\partial\:x}((x_{1}+x_{2})^{2})
area \sqrt[3]{x}, 1/x ,1,27	area\:\sqrt[3]{x},\frac{1}{x},1,27
integral from 0 to 9 of pi(y^{3/2})^2	\int\:_{0}^{9}π(y^{\frac{3}{2}})^{2}dy
sum from n=0 to infinity of (5^n)/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{5^{n}}{4^{n}}
derivative of (x^{7/3}+3x^3-8/(6x^2))	\frac{d}{dx}(\frac{x^{\frac{7}{3}}+3x^{3}-8}{6x^{2}})
limit as x approaches 0 of (x+tan(x))/x	\lim\:_{x\to\:0}(\frac{x+\tan(x)}{x})
derivative of x^v	\frac{d}{dx}(x^{v})
integral of (1+x+x^2)/(sqrt(x))	\int\:\frac{1+x+x^{2}}{\sqrt{x}}dx
integral of (ln(x))/(x^a)	\int\:\frac{\ln(x)}{x^{a}}dx
integral of ((3x^2+2))/(x-1)	\int\:\frac{(3x^{2}+2)}{x-1}dx
integral of sin(3x)sin(kx)	\int\:\sin(3x)\sin(kx)dx
integral of (3x-4)^7	\int\:(3x-4)^{7}dx
inverse oflaplace (-s-1)/(s^2+s+10)	inverselaplace\:\frac{-s-1}{s^{2}+s+10}
integral of-xcos((npix)/2)	\int\:-x\cos(\frac{nπx}{2})dx
derivative of tan(xcot(x))	\frac{d}{dx}(\tan(x)\cot(x))

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