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Popular Calculus Problems

y^'=xy	y^{\prime\:}=xy
derivative of 7x^2-12x	\frac{d}{dx}(7x^{2}-12x)
derivative of sqrt(3/2 x-5)	\frac{d}{dx}(\sqrt{\frac{3}{2}x-5})
derivative of \sqrt[9]{x^8}-x^pi	derivative\:\sqrt[9]{x^{8}}-x^{π}
limit as x approaches 0 of (\|6x\|)/(3x)	\lim\:_{x\to\:0}(\frac{\left\|6x\right\|}{3x})
y^{'''}-2y^{''}+2y^'=0	y^{\prime\:\prime\:\prime\:}-2y^{\prime\:\prime\:}+2y^{\prime\:}=0
derivative of 7x^2-4x	\frac{d}{dx}(7x^{2}-4x)
derivative of f(x)=(x^5-5x^2)/(2x^5+5x)	derivative\:f(x)=\frac{x^{5}-5x^{2}}{2x^{5}+5x}
(\partial)/(\partial x)(3xz^3e^{y^2})	\frac{\partial\:}{\partial\:x}(3xz^{3}e^{y^{2}})
integral of (ln(2x))^2	\int\:(\ln(2x))^{2}dx
limit as x approaches-3 of 2/(x+2)	\lim\:_{x\to\:-3}(\frac{2}{x+2})
integral of x(sqrt(x+3))	\int\:x(\sqrt{x+3})dx
derivative of x/(x-6)	derivative\:\frac{x}{x-6}
derivative of f(x)=(x^3+1)e^x	derivative\:f(x)=(x^{3}+1)e^{x}
integral from 1 to 3 of (x^2+2x-2)	\int\:_{1}^{3}(x^{2}+2x-2)dx
integral of x^2(4x+7)	\int\:x^{2}(4x+7)dx
derivative of 20xe^{-x}	\frac{d}{dx}(20xe^{-x})
(\partial)/(\partial y)(2y^2sqrt(x))	\frac{\partial\:}{\partial\:y}(2y^{2}\sqrt{x})
derivative of f(x)=(4x+3)/(sqrt(x))	derivative\:f(x)=\frac{4x+3}{\sqrt{x}}
laplacetransform sin(2t)cos(2t)	laplacetransform\:\sin(2t)\cos(2t)
slope of (1950,53700),(2000,142000)	slope\:(1950,53700),(2000,142000)
derivative of f(x)=\sqrt[3]{x},x=27	derivative\:f(x)=\sqrt[3]{x},x=27
y^'=xy^2-y/x	y^{\prime\:}=xy^{2}-\frac{y}{x}
y^'=(64xy)^{1/3}	y^{\prime\:}=(64xy)^{\frac{1}{3}}
integral from 1 to infinity of 1/(y^2)	\int\:_{1}^{\infty\:}\frac{1}{y^{2}}dy
derivative of y= x/2	derivative\:y=\frac{x}{2}
derivative of 9/(x^3)	derivative\:\frac{9}{x^{3}}
integral of ((3x^2+7x+3))/(x(x+1)^2)	\int\:\frac{(3x^{2}+7x+3)}{x(x+1)^{2}}dx
(\partial)/(\partial x)((sin(y))/(x^2+1))	\frac{\partial\:}{\partial\:x}(\frac{\sin(y)}{x^{2}+1})
integral of sqrt(10x-x^2)	\int\:\sqrt{10x-x^{2}}dx
inverse oflaplace 3/((s^2+9))	inverselaplace\:\frac{3}{(s^{2}+9)}
taylor 1/x ,-1	taylor\:\frac{1}{x},-1
integral of (3x^5)/(sqrt(5-12x^6))	\int\:\frac{3x^{5}}{\sqrt{5-12x^{6}}}dx
integral from 1 to e of 2/x	\int\:_{1}^{e}\frac{2}{x}dx
integral of (-1)^n	\int\:(-1)^{n}
(\partial)/(\partial x)(tan(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\tan(x^{2}+y^{2}))
f(x)=-8sin(4x)-0.4e^{-0.2x}	f(x)=-8\sin(4x)-0.4e^{-0.2x}
limit as x approaches-9 of 8/(x+9)	\lim\:_{x\to\:-9}(\frac{8}{x+9})
(\partial)/(\partial y)(xy+2x-ln(x^2y))	\frac{\partial\:}{\partial\:y}(xy+2x-\ln(x^{2}y))
integral from 0 to 1 of (sin(pix))^2	\int\:_{0}^{1}(\sin(πx))^{2}dx
integral of (9x^2-4x)e^{2x}	\int\:(9x^{2}-4x)e^{2x}dx
integral of e^{-4x}x	\int\:e^{-4x}xdx
integral of (2x+3)/(2x+1)	\int\:\frac{2x+3}{2x+1}dx
(\partial)/(\partial y)(e^{x+y})	\frac{\partial\:}{\partial\:y}(e^{x+y})
limit as x approaches 2 of sqrt(9-x^2)	\lim\:_{x\to\:2}(\sqrt{9-x^{2}})
sum from n=1 to infinity of 7/(n^2+4)	\sum\:_{n=1}^{\infty\:}\frac{7}{n^{2}+4}
limit as x approaches 0 of (9^x-7^x)/x	\lim\:_{x\to\:0}(\frac{9^{x}-7^{x}}{x})
integral from 1 to 7 of 1/(sqrt(2x+2))	\int\:_{1}^{7}\frac{1}{\sqrt{2x+2}}dx
derivative of tan^2(x^3)	\frac{d}{dx}(\tan^{2}(x^{3}))
area x+1y=3,x+9=y^2	area\:x+1y=3,x+9=y^{2}
integral of (x^3+x^2)/(x^2-9x+20)	\int\:\frac{x^{3}+x^{2}}{x^{2}-9x+20}dx
area 6-x^2,x^2-2,0,3	area\:6-x^{2},x^{2}-2,0,3
integral of (pi/2-5x^{-0.5})	\int\:(\frac{π}{2}-5x^{-0.5})dx
derivative of (1+x^3)	\frac{d}{dx}((1+x)^{3})
integral of (e^{-x})/(e^x-1)	\int\:\frac{e^{-x}}{e^{x}-1}dx
y^'=-(4t)/y	y^{\prime\:}=-\frac{4t}{y}
limit as x approaches-1 of (x^2-5)/(1-x)	\lim\:_{x\to\:-1}(\frac{x^{2}-5}{1-x})
derivative of arctan(x-sqrt(x^2+1))	\frac{d}{dx}(\arctan(x-\sqrt{x^{2}+1}))
integral of (1+sin(x))^2	\int\:(1+\sin(x))^{2}dx
(x^2+y^2+x)dx+xydy=0	(x^{2}+y^{2}+x)dx+xydy=0
integral of y/(y^3-1)	\int\:\frac{y}{y^{3}-1}dy
integral of xe^{-2y}	\int\:xe^{-2y}dx
(\partial)/(\partial x)(x*e^{y/z})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{\frac{y}{z}})
sum from n=1 to infinity of n/(n^5+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{5}+1}
(\partial)/(\partial x)(z-x^2-y^2)	\frac{\partial\:}{\partial\:x}(z-x^{2}-y^{2})
integral of 1/(8+3x)	\int\:\frac{1}{8+3x}dx
taylor sin(5x)	taylor\:\sin(5x)
(\partial)/(\partial x)(xsin(2y+x))	\frac{\partial\:}{\partial\:x}(x\sin(2y+x))
derivative of (x-9/(7x^2e^x))	\frac{d}{dx}(\frac{x-9}{7x^{2}e^{x}})
(dy}{dx}= 1/4 e^x-y/x+\frac{3x)/4	\frac{dy}{dx}=\frac{1}{4}e^{x}-\frac{y}{x}+\frac{3x}{4}
integral of (4-32x)/(sqrt(1-16x^2))	\int\:\frac{4-32x}{\sqrt{1-16x^{2}}}dx
implicit x^2+4y^2=4	implicit\:x^{2}+4y^{2}=4
implicit (dy)/(dx),y=x^3	implicit\:\frac{dy}{dx},y=x^{3}
y^'+y=e^x,y(0)=1	y^{\prime\:}+y=e^{x},y(0)=1
tangent of e^x+1	tangent\:e^{x}+1
(e^{5x})^'	(e^{5x})^{\prime\:}
limit as x approaches 2+of (x-3)^2	\lim\:_{x\to\:2+}((x-3)^{2})
integral of (x^2-5x+6)/((2x-1)(x-2)^2)	\int\:\frac{x^{2}-5x+6}{(2x-1)(x-2)^{2}}dx
limit as x approaches infinity of x^3-3	\lim\:_{x\to\:\infty\:}(x^{3}-3)
derivative of log_{2}(n)	derivative\:\log_{2}(n)
derivative of 10cos(2x)	\frac{d}{dx}(10\cos(2x))
(\partial)/(\partial x)(2(x+1))	\frac{\partial\:}{\partial\:x}(2(x+1))
integral of 9/(x(x^2+1))	\int\:\frac{9}{x(x^{2}+1)}dx
integral of x^2-2x+3	\int\:x^{2}-2x+3dx
derivative of sec(5/6)x^3	derivative\:\sec(\frac{5}{6})x^{3}
(\partial)/(\partial x)(-e^{kz}Awsin(kx-wt))	\frac{\partial\:}{\partial\:x}(-e^{kz}Aw\sin(kx-wt))
(\partial)/(\partial x)(e^{4xe^y})	\frac{\partial\:}{\partial\:x}(e^{4xe^{y}})
limit as x approaches 1-of 2/x-1/(ln(x))	\lim\:_{x\to\:1-}(\frac{2}{x}-\frac{1}{\ln(x)})
integral of (-x+2)/(x^2+2x+4)	\int\:\frac{-x+2}{x^{2}+2x+4}dx
(dy)/(dx)=e^{-2y}tan^2(x)	\frac{dy}{dx}=e^{-2y}\tan^{2}(x)
x^{''}+x^'-2x=0	x^{\prime\:\prime\:}+x^{\prime\:}-2x=0
y^'=-y/x	y^{\prime\:}=-\frac{y}{x}
x^{'''}+x^{''}+3x^'-5x=0	x^{\prime\:\prime\:\prime\:}+x^{\prime\:\prime\:}+3x^{\prime\:}-5x=0
derivative of e^{x^2+1}	derivative\:e^{x^{2}+1}
derivative of f(x)=e^{4/x}	derivative\:f(x)=e^{\frac{4}{x}}
derivative of (5x)/(x+4)	derivative\:\frac{5x}{x+4}
integral of (1/(1+x))	\int\:(\frac{1}{1+x})dx
derivative of f(x)=e^{-ax}cos(bx-c)	derivative\:f(x)=e^{-ax}\cos(bx-c)
integral from-2 to 3 of (46)/(x^4)	\int\:_{-2}^{3}\frac{46}{x^{4}}dx
derivative of x(-1/5)	derivative\:x(-\frac{1}{5})

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