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Popular Calculus Problems

derivative of 3/(x^4)	\frac{d}{dx}(\frac{3}{x^{4}})
(\partial)/(\partial x)(sqrt(7-x^5-y^3))	\frac{\partial\:}{\partial\:x}(\sqrt{7-x^{5}-y^{3}})
(\partial)/(\partial u)(x^5v^2+2y^3u-3)	\frac{\partial\:}{\partial\:u}(x^{5}v^{2}+2y^{3}u-3)
(\partial)/(\partial x)(sqrt(61-x^2-3y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{61-x^{2}-3y^{2}})
integral from 2 to 5 of x^2	\int\:_{2}^{5}x^{2}dx
limit as x approaches 0+of 7sin(x)ln(x)	\lim\:_{x\to\:0+}(7\sin(x)\ln(x))
integral of sin(11x)ln(sin(11x))	\int\:\sin(11x)\ln(\sin(11x))dx
tangent of f(x)=x^3-2x+1,\at x=0	tangent\:f(x)=x^{3}-2x+1,\at\:x=0
expand 8/((1-x)^2)	expand\:\frac{8}{(1-x)^{2}}
integral of (3(x+2))/((x+7)^4)	\int\:\frac{3(x+2)}{(x+7)^{4}}dx
derivative of cos^2(pix)	\frac{d}{dx}(\cos^{2}(πx))
integral from 0 to 1 of-(5y)/(e^{2y)}	\int\:_{0}^{1}-\frac{5y}{e^{2y}}dy
area-x^3+x,x=-1,y=-1/2	area\:-x^{3}+x,x=-1,y=-\frac{1}{2}
integral of (5x+1)/(x^2+4x+5)	\int\:\frac{5x+1}{x^{2}+4x+5}dx
integral from 0 to 5 of 2/(x^2)	\int\:_{0}^{5}\frac{2}{x^{2}}dx
(dy)/(dt)=-y/t-7	\frac{dy}{dt}=-\frac{y}{t}-7
derivative of 2/((1-x^3))	\frac{d}{dx}(\frac{2}{(1-x)^{3}})
(\partial)/(\partial x)(z*log_{e}(x^2+y^2))	\frac{\partial\:}{\partial\:x}(z\cdot\:\log_{e}(x^{2}+y^{2}))
derivative of (6x^4-9x^2+8)^4	derivative\:(6x^{4}-9x^{2}+8)^{4}
limit as x approaches-1-of x^2+1	\lim\:_{x\to\:-1-}(x^{2}+1)
derivative of ln(e^{2x})	derivative\:\ln(e^{2x})
area y=(x+3)^2,(0,1)	area\:y=(x+3)^{2},(0,1)
derivative of cos(1-x^2)	\frac{d}{dx}(\cos(1-x^{2}))
integral of ((1+x+x^2)/(sqrt(x)))	\int\:(\frac{1+x+x^{2}}{\sqrt{x}})dx
derivative of f(x)=\sqrt[7]{t}-7e^t	derivative\:f(x)=\sqrt[7]{t}-7e^{t}
integral of 1/a	\int\:\frac{1}{a}da
simplify (4x^3+3x^2)/x	simplify\:\frac{4x^{3}+3x^{2}}{x}
derivative of f(t)=t^2+5	derivative\:f(t)=t^{2}+5
derivative of f(x)=(-3x^3-1)/(2x^2+1)	derivative\:f(x)=\frac{-3x^{3}-1}{2x^{2}+1}
derivative of xy-y^2	\frac{d}{dx}(xy-y^{2})
integral of (5x^3-4x+2)/(x^3-x^2)	\int\:\frac{5x^{3}-4x+2}{x^{3}-x^{2}}dx
x(dy)/(dx)+y=2x+1,y(1)=6	x\frac{dy}{dx}+y=2x+1,y(1)=6
limit as x approaches 1 of 3*a+x	\lim\:_{x\to\:1}(3\cdot\:a+x)
(\partial)/(\partial y)(10xzsin(y))	\frac{\partial\:}{\partial\:y}(10xz\sin(y))
integral of 1/((121+x^2)^{3/2)}	\int\:\frac{1}{(121+x^{2})^{\frac{3}{2}}}dx
y^'=7sqrt(x)y	y^{\prime\:}=7\sqrt{x}y
e^{0.75t}y^'+0.75ye^{0.75t}=-0.00003e^{0.75t}	e^{0.75t}y^{\prime\:}+0.75ye^{0.75t}=-0.00003e^{0.75t}
derivative of f(x)=-3cos(x)+2sin(x)	derivative\:f(x)=-3\cos(x)+2\sin(x)
(\partial)/(\partial x)(7x^6y^4+8x^5y^7)	\frac{\partial\:}{\partial\:x}(7x^{6}y^{4}+8x^{5}y^{7})
integral of ((2x^2-x+4))/(x^3+4x)	\int\:\frac{(2x^{2}-x+4)}{x^{3}+4x}dx
limit as x approaches 2 of (x^3+x^2-8x-12)/(x^4+4x^3+5x^2+4x+4)	\lim\:_{x\to\:2}(\frac{x^{3}+x^{2}-8x-12}{x^{4}+4x^{3}+5x^{2}+4x+4})
(\partial)/(\partial x)(z^3-xy+yz+y^3-2)	\frac{\partial\:}{\partial\:x}(z^{3}-xy+yz+y^{3}-2)
inverse oflaplace 4/([s(s^2+4)])	inverselaplace\:\frac{4}{[s(s^{2}+4)]}
y^'=((t^4+y^4))/(ty^3)	y^{\prime\:}=\frac{(t^{4}+y^{4})}{ty^{3}}
integral of (3-x)/(x^2-1)	\int\:\frac{3-x}{x^{2}-1}dx
limit as x approaches-1-of (x-2)/(x^2-1)	\lim\:_{x\to\:-1-}(\frac{x-2}{x^{2}-1})
limit as x approaches+0 of x	\lim\:_{x\to\:+0}(x)
laplacetransform e^{2x}	laplacetransform\:e^{2x}
integral of (2x+3)^4	\int\:(2x+3)^{4}dx
integral of e^{uv}	\int\:e^{uv}du
derivative of 4x^5-10x^4+2	\frac{d}{dx}(4x^{5}-10x^{4}+2)
derivative of (x^2+x+4/(x+1))	\frac{d}{dx}(\frac{x^{2}+x+4}{x+1})
integral of (x^5-3x)/(x^4)	\int\:\frac{x^{5}-3x}{x^{4}}dx
integral of 4y+2x-5	\int\:4y+2x-5dx
area y=x^2+1,x=0,x=6	area\:y=x^{2}+1,x=0,x=6
integral of-4sin(2x)+3	\int\:-4\sin(2x)+3dx
derivative of (6x-1/(4x+5))	\frac{d}{dx}(\frac{6x-1}{4x+5})
integral of 1/(sqrt(2x+3))	\int\:\frac{1}{\sqrt{2x+3}}dx
derivative of (1/2 x^2-3^2)	\frac{d}{dx}((\frac{1}{2}x^{2}-3)^{2})
x^2(dy)/(dx)=(x+1)y	x^{2}\frac{dy}{dx}=(x+1)y
area y=xe^{-x},y=0,x=4	area\:y=xe^{-x},y=0,x=4
limit as x approaches+1 of (x^2-9)^{1/3}	\lim\:_{x\to\:+1}((x^{2}-9)^{\frac{1}{3}})
(d^2}{dx^2}(\frac{ln(x))/x)	\frac{d^{2}}{dx^{2}}(\frac{\ln(x)}{x})
derivative of 2+e^x	\frac{d}{dx}(2+e^{x})
(dy)/(dt)=((te^t))/(ysqrt(1+y^2))	\frac{dy}{dt}=\frac{(te^{t})}{y\sqrt{1+y^{2}}}
integral of (e^{3x})/(9+e^{6x)}	\int\:\frac{e^{3x}}{9+e^{6x}}dx
limit as x approaches 3 of 10^{x^2-4x}	\lim\:_{x\to\:3}(10^{x^{2}-4x})
integral of sin(t)+cos(t)	\int\:\sin(t)+\cos(t)dt
15x^2-4y^'=0	15x^{2}-4y^{\prime\:}=0
(\partial)/(\partial x)(y/(h^2x))	\frac{\partial\:}{\partial\:x}(\frac{y}{h^{2}x})
y^'=2y(1-3y)	y^{\prime\:}=2y(1-3y)
ty^'-y=0	ty^{\prime\:}-y=0
area ln(x),y=2,1,e^2	area\:\ln(x),y=2,1,e^{2}
derivative of 3sqrt(4-x)	\frac{d}{dx}(3\sqrt{4-x})
(dr)/(dt)=-4rt	\frac{dr}{dt}=-4rt
derivative of 6pir^2	derivative\:6πr^{2}
integral of 1/((x^2+2))	\int\:\frac{1}{(x^{2}+2)}dx
integral of (-3x^3+2x^2-28x+10)/(x^2+9)	\int\:\frac{-3x^{3}+2x^{2}-28x+10}{x^{2}+9}dx
derivative of y^2-x	\frac{d}{dx}(y^{2}-x)
integral of x^4(x^5-5)^3	\int\:x^{4}(x^{5}-5)^{3}dx
derivative of f(x)=log_{e}(x)	derivative\:f(x)=\log_{e}(x)
integral of (x^2)/(x^2-1)	\int\:\frac{x^{2}}{x^{2}-1}dx
(\partial)/(\partial x)(x^{2/3}y^{1/3})	\frac{\partial\:}{\partial\:x}(x^{\frac{2}{3}}y^{\frac{1}{3}})
derivative of (1+x^2^2)	\frac{d}{dx}((1+x^{2})^{2})
derivative of (2x^4-6x^2+5^2)	\frac{d}{dx}((2x^{4}-6x^{2}+5)^{2})
-y+y^'-y=e^xcos(x)	-y+y^{\prime\:}-y=e^{x}\cos(x)
implicit (d^2y)/(dx^2),xy+7ey(x)=7e	implicit\:\frac{d^{2}y}{dx^{2}},xy+7ey(x)=7e
derivative of f(x)=tan(x)-1sec(x)	derivative\:f(x)=\tan(x)-1\sec(x)
derivative of f(x)=\sqrt[3]{x+2}	derivative\:f(x)=\sqrt[3]{x+2}
(\partial)/(\partial x)(ln(13x^2-10y^2))	\frac{\partial\:}{\partial\:x}(\ln(13x^{2}-10y^{2}))
(\partial)/(\partial x)(x^2y^3sin(x-2y))	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}\sin(x-2y))
derivative of (2xcos(x^2)/(sin(x^2)+1))	\frac{d}{dx}(\frac{2x\cos(x^{2})}{\sin(x^{2})+1})
integral of x/(sqrt(a^2-x^2))	\int\:\frac{x}{\sqrt{a^{2}-x^{2}}}dx
limit as x approaches 25 of sqrt(x)	\lim\:_{x\to\:25}(\sqrt{x})
derivative of f(x)=7e^x	derivative\:f(x)=7e^{x}
integral of x/(x^2-16)	\int\:\frac{x}{x^{2}-16}dx
derivative of-8/x	derivative\:-\frac{8}{x}
(x+y)(dy)/(dx)=1	(x+y)\frac{dy}{dx}=1
sum from n=1 to infinity of n^{-1}	\sum\:_{n=1}^{\infty\:}n^{-1}
area-x^2+9,-2x^2+18	area\:-x^{2}+9,-2x^{2}+18

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