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Popular Calculus Problems

derivative of 5/(\sqrt[4]{x})	\frac{d}{dx}(\frac{5}{\sqrt[4]{x}})
(\partial)/(\partial x)(x^2+2y^3)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{3})
(dy)/(dx)=((y^2+2xsqrt(x^2+y^2)))/(xy)	\frac{dy}{dx}=\frac{(y^{2}+2x\sqrt{x^{2}+y^{2}})}{xy}
inverse oflaplace s/(s^2+7s+2)	inverselaplace\:\frac{s}{s^{2}+7s+2}
integral of 3cos(x/3)	\int\:3\cos(\frac{x}{3})dx
derivative of 4xe^{4x}	\frac{d}{dx}(4xe^{4x})
limit as x approaches 0-of x^2-7/x	\lim\:_{x\to\:0-}(x^{2}-\frac{7}{x})
integral of 4(x-1)in(x-1)	\int\:4(x-1)in(x-1)dx
f(x)=(xcos(pix)+1)/(x-1)	f(x)=\frac{x\cos(πx)+1}{x-1}
tangent of (3x+13)^{1/2}	tangent\:(3x+13)^{\frac{1}{2}}
derivative of {f}(x(2x))	\frac{d}{dx}({f}(x)(2x))
integral from-1 to 1 of e^x-x^2+6	\int\:_{-1}^{1}e^{x}-x^{2}+6dx
limit as x approaches 5 of (2-25)/(x-5)	\lim\:_{x\to\:5}(\frac{2-25}{x-5})
sum from n=1 to infinity of 1/(e^{n+1)}	\sum\:_{n=1}^{\infty\:}\frac{1}{e^{n+1}}
slope of (3,-4),(5,1)	slope\:(3,-4),(5,1)
integral of (x+2)/(x^2-1)	\int\:\frac{x+2}{x^{2}-1}dx
derivative of cos(2θ)	derivative\:\cos(2θ)
limit as x approaches 0 of 8/(\frac{2+e^1){x}}	\lim\:_{x\to\:0}(\frac{8}{\frac{2+e^{1}}{x}})
tangent of f(x)=14xsin(x),\at x= pi/2	tangent\:f(x)=14x\sin(x),\at\:x=\frac{π}{2}
integral of (11x^2)/((25+x^2)^2)	\int\:\frac{11x^{2}}{(25+x^{2})^{2}}dx
derivative of 1/x-1	\frac{d}{dx}(\frac{1}{x}-1)
integral of 1/((1+u^2))	\int\:\frac{1}{(1+u^{2})}du
integral of 30(x+2)(x+3)^4	\int\:30(x+2)(x+3)^{4}dx
derivative of f(x)=x^4-3x^3-9x^2+5x	derivative\:f(x)=x^{4}-3x^{3}-9x^{2}+5x
integral from 0 to pi/2 of (sin(x))	\int\:_{0}^{\frac{π}{2}}(\sin(x))dx
y^{''}-7y^'+12y=-2cos(3t)	y^{\prime\:\prime\:}-7y^{\prime\:}+12y=-2\cos(3t)
(1+x^5)y^'+5x^4y=13x^4	(1+x^{5})y^{\prime\:}+5x^{4}y=13x^{4}
integral of ((x-3))/x	\int\:\frac{(x-3)}{x}dx
(\partial)/(\partial y)(sin(x)*cos(y))	\frac{\partial\:}{\partial\:y}(\sin(x)\cdot\:\cos(y))
derivative of (\sqrt[3]{x})/(x-6)	derivative\:\frac{\sqrt[3]{x}}{x-6}
derivative of f(x)=x^2e^x-2xe^x+9e^x	derivative\:f(x)=x^{2}e^{x}-2xe^{x}+9e^{x}
sum from n=8 to infinity of 1/(n(n-1))	\sum\:_{n=8}^{\infty\:}\frac{1}{n(n-1)}
integral from 0 to 1 of (x^2-4x+7)	\int\:_{0}^{1}(x^{2}-4x+7)dx
derivative of-3sin(x)	\frac{d}{dx}(-3\sin(x))
limit as x approaches 4 of (x+1)/(x+4)	\lim\:_{x\to\:4}(\frac{x+1}{x+4})
integral of x^2cos(1/6 x)	\int\:x^{2}\cos(\frac{1}{6}x)dx
(dy)/(dx)=6e^{2x-y}	\frac{dy}{dx}=6e^{2x-y}
integral from 0 to pi of xcos(x)	\int\:_{0}^{π}x\cos(x)dx
(\partial)/(\partial z)(4ze^{xyz})	\frac{\partial\:}{\partial\:z}(4ze^{xyz})
derivative of f(2)=(3x+2)/(x-1)	derivative\:f(2)=\frac{3x+2}{x-1}
integral of sin^4(3x)cos^2(3x)	\int\:\sin^{4}(3x)\cos^{2}(3x)dx
(\partial)/(\partial x)((8+23x)y^{tan(x)})	\frac{\partial\:}{\partial\:x}((8+23x)y^{\tan(x)})
f(t)=ln(t^2+3)	f(t)=\ln(t^{2}+3)
limit as x approaches 0 of (sqrt(1+7x)-sqrt(1-5x))/x	\lim\:_{x\to\:0}(\frac{\sqrt{1+7x}-\sqrt{1-5x}}{x})
tangent of f(x)= 1/(x^6),(3, 1/729)	tangent\:f(x)=\frac{1}{x^{6}},(3,\frac{1}{729})
sum from n=1 to infinity of (n!)/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{3^{n}}
limit as x approaches 0 of (10^x-11^x)/x	\lim\:_{x\to\:0}(\frac{10^{x}-11^{x}}{x})
integral from-2 to 2 of (2-\|x\|)	\int\:_{-2}^{2}(2-\left\|x\right\|)dx
limit as x approaches 0-of-3x^2+2x	\lim\:_{x\to\:0-}(-3x^{2}+2x)
integral from 0 to l of xsin^2((pix)/l)	\int\:_{0}^{l}x\sin^{2}(\frac{πx}{l})dx
slope of (5.1)(3.6)	slope\:(5.1)(3.6)
integral of (7x+2)/(x^2-4)	\int\:\frac{7x+2}{x^{2}-4}dx
derivative of ((e^x-e^{-x})/((e^x+e^{-x))})	\frac{d}{dx}(\frac{(e^{x}-e^{-x})}{(e^{x}+e^{-x})})
integral of e^xsin^2(x)	\int\:e^{x}\sin^{2}(x)dx
(dy)/(dx)= x/y	\frac{dy}{dx}=\frac{x}{y}
derivative of (10x+4x^2)/((5+4x)^2)	derivative\:\frac{10x+4x^{2}}{(5+4x)^{2}}
derivative of \sqrt[3]{3tan(x^2})	\frac{d}{dx}(\sqrt[3]{3\tan(x^{2})})
integral of 4-2x	\int\:4-2xdx
integral of (x^2)/2+x	\int\:\frac{x^{2}}{2}+xdx
(\partial)/(\partial x)(x*sin(xy))	\frac{\partial\:}{\partial\:x}(x\cdot\:\sin(xy))
integral of 5x^{1/3}+4x^{-1/3}+11	\int\:5x^{\frac{1}{3}}+4x^{-\frac{1}{3}}+11dx
derivative of ((sqrt(x)^3)/((2x^7+x)^2))	\frac{d}{dx}(\frac{(\sqrt{x})^{3}}{(2x^{7}+x)^{2}})
derivative of (x^2+2^5)	\frac{d}{dx}((x^{2}+2)^{5})
limit as x approaches 4-of (x-4)/(\|x-4\|)	\lim\:_{x\to\:4-}(\frac{x-4}{\left\|x-4\right\|})
y^2+2x+2xyy^'=0	y^{2}+2x+2xyy^{\prime\:}=0
(dr)/(dθ)+rtan(θ)=tan(θ)	\frac{dr}{dθ}+r\tan(θ)=\tan(θ)
derivative of (sin(x^2)/(x^3))	\frac{d}{dx}(\frac{\sin(x^{2})}{x^{3}})
2(sin(t)y^'+cos(t)y)=cos(t)sin^3(t)	2(\sin(t)y^{\prime\:}+\cos(t)y)=\cos(t)\sin^{3}(t)
derivative of f(x)=e^{x^4}	derivative\:f(x)=e^{x^{4}}
derivative of f(x)=sqrt(3+5sin(x))	derivative\:f(x)=\sqrt{3+5\sin(x)}
integral of (\sqrt[3]{1+ln(x)})(x^{-1})	\int\:(\sqrt[3]{1+\ln(x)})(x^{-1})dx
integral of (x^2)/(sqrt(441-x^2))	\int\:\frac{x^{2}}{\sqrt{441-x^{2}}}dx
integral of p(p+3)^5	\int\:p(p+3)^{5}dp
integral of 9sec^6(t)	\int\:9\sec^{6}(t)dt
integral from 0 to pi/2 of cos^3(3x)	\int\:_{0}^{\frac{π}{2}}\cos^{3}(3x)dx
(sinh(t))^'	(\sinh(t))^{\prime\:}
derivative of \sqrt[3]{x}*(x-2)/(x+1)	derivative\:\sqrt[3]{x}\cdot\:\frac{x-2}{x+1}
integral of 2x^3sqrt(x^2-2)	\int\:2x^{3}\sqrt{x^{2}-2}dx
derivative of 2x-1/x	derivative\:2x-\frac{1}{x}
(dy)/(dt)=y^2-2y-2	\frac{dy}{dt}=y^{2}-2y-2
(\partial)/(\partial x)(y^4cos(6x))	\frac{\partial\:}{\partial\:x}(y^{4}\cos(6x))
integral of (x^2)/(x^2+x+2)	\int\:\frac{x^{2}}{x^{2}+x+2}dx
integral of (e^x)/(sqrt(4-9e^{2x))}	\int\:\frac{e^{x}}{\sqrt{4-9e^{2x}}}dx
(\partial)/(\partial x)(5-x^4+2x^2-y^2)	\frac{\partial\:}{\partial\:x}(5-x^{4}+2x^{2}-y^{2})
derivative of (cos(9x))^x	derivative\:(\cos(9x))^{x}
48y^{''}+34y^'-5y=0	48y^{\prime\:\prime\:}+34y^{\prime\:}-5y=0
derivative of (4x-3^2)	\frac{d}{dx}((4x-3)^{2})
area x^{(4/3)},2x^{(1/3)},0,2	area\:x^{(\frac{4}{3})},2x^{(\frac{1}{3})},0,2
(e^y+1)^2e^{-y}dx+(e^x+1)^5e^{-x}dy=0	(e^{y}+1)^{2}e^{-y}dx+(e^{x}+1)^{5}e^{-x}dy=0
integral of (sec(x))/(sec(x)-tan(x))	\int\:\frac{\sec(x)}{\sec(x)-\tan(x)}dx
limit as x approaches 0-of arcsin(e^x)	\lim\:_{x\to\:0-}(\arcsin(e^{x}))
area y=6x^2-2x,y=x^3-6x+5	area\:y=6x^{2}-2x,y=x^{3}-6x+5
derivative of 3x^2(x^3-2x)	\frac{d}{dx}(3x^{2}(x^{3}-2x))
integral from 1 to e^2 of 2/x	\int\:_{1}^{e^{2}}\frac{2}{x}dx
derivative of 1.58e^{-0.213x}	\frac{d}{dx}(1.58e^{-0.213x})
integral of (2x-1)/(x^2-8x+15)	\int\:\frac{2x-1}{x^{2}-8x+15}dx
integral of (x+4)/(5x+5)	\int\:\frac{x+4}{5x+5}dx
integral of sin^5(2t)cos^2(2t)	\int\:\sin^{5}(2t)\cos^{2}(2t)dt
derivative of 1/(8sqrt(x))	\frac{d}{dx}(\frac{1}{8\sqrt{x}})
integral of-te^t	\int\:-te^{t}dt

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