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Popular Calculus Problems

(\partial)/(\partial y)(cos(xy))	\frac{\partial\:}{\partial\:y}(\cos(xy))
integral from 0 to 3 of sqrt(1+x^4)	\int\:_{0}^{3}\sqrt{1+x^{4}}dx
limit as x approaches 5 of 2x^2	\lim\:_{x\to\:5}(2x^{2})
simplify 1/((z-1)^3)*1/(e^{z+1)}	simplify\:\frac{1}{(z-1)^{3}}\cdot\:\frac{1}{e^{z+1}}
(dy)/(dx)=(x^2-3y^2)/(2xy)	\frac{dy}{dx}=\frac{x^{2}-3y^{2}}{2xy}
d/(dy)(y-y/(x^2)e^{y/x})	\frac{d}{dy}(y-\frac{y}{x^{2}}e^{\frac{y}{x}})
derivative of 5sin(pi/4)	derivative\:5\sin(\frac{π}{4})
derivative of y/(x-y)	\frac{d}{dx}(\frac{y}{x-y})
tangent of f(x)= 1/(3+2x),(2, 1/7)	tangent\:f(x)=\frac{1}{3+2x},(2,\frac{1}{7})
integral of 3sin^3(x)cos^5(x)	\int\:3\sin^{3}(x)\cos^{5}(x)dx
derivative of (8x^2+6x+2)/(sqrt(x))	derivative\:\frac{8x^{2}+6x+2}{\sqrt{x}}
derivative of y=(arctan(4x))^2	derivative\:y=(\arctan(4x))^{2}
integral of (x-2)/(x^2)	\int\:\frac{x-2}{x^{2}}dx
derivative of xe^{xy}	\frac{d}{dx}(xe^{xy})
derivative of 8x^{-3}	\frac{d}{dx}(8x^{-3})
derivative of x/(11)-(11)/x	derivative\:\frac{x}{11}-\frac{11}{x}
integral from 0 to 2*pi of sin(t)	\int\:_{0}^{2\cdot\:π}\sin(t)dt
derivative of 3x+x^2	\frac{d}{dx}(3x+x^{2})
integral of 4xcos(9x)	\int\:4x\cos(9x)dx
derivative of 1/8 ln((3x-4/(3x+4)))	\frac{d}{dx}(\frac{1}{8}\ln(\frac{3x-4}{3x+4}))
(\partial)/(\partial x)(-x^3+4xy-2y^2+1)	\frac{\partial\:}{\partial\:x}(-x^{3}+4xy-2y^{2}+1)
limit as x approaches 7 of 2x+5	\lim\:_{x\to\:7}(2x+5)
derivative of (x+4^2)	\frac{d}{dx}((x+4)^{2})
integral of (5x-1)^7	\int\:(5x-1)^{7}dx
area 2x,9x-x^2,(7,14)	area\:2x,9x-x^{2},(7,14)
derivative of f(x)= 6/(ln(x^2+4))	derivative\:f(x)=\frac{6}{\ln(x^{2}+4)}
integral of (sin(44x))/(1+cos^2(44x))	\int\:\frac{\sin(44x)}{1+\cos^{2}(44x)}dx
integral of 2x(x^2+1)^{-7}	\int\:2x(x^{2}+1)^{-7}dx
area f(x)=x^2,[0,3]	area\:f(x)=x^{2},[0,3]
integral from-1 to 3 of (x^2+6x+3)	\int\:_{-1}^{3}(x^{2}+6x+3)dx
(d^3)/(dx^3)(x^4-10x^3)	\frac{d^{3}}{dx^{3}}(x^{4}-10x^{3})
(\partial)/(\partial x)(1/(y+z))	\frac{\partial\:}{\partial\:x}(\frac{1}{y+z})
derivative of f(x)= 5/(x^5)	derivative\:f(x)=\frac{5}{x^{5}}
y^{''}+2y^'+y=e^{-t}+9e^{5t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=e^{-t}+9e^{5t}
limit as n approaches infinity of i/n	\lim\:_{n\to\:\infty\:}(\frac{i}{n})
taylor (1+z)^{1/4}	taylor\:(1+z)^{\frac{1}{4}}
derivative of sqrt(5)x	\frac{d}{dx}(\sqrt{5}x)
(\partial)/(\partial x)(y^2-cos(x)y)	\frac{\partial\:}{\partial\:x}(y^{2}-\cos(x)y)
derivative of 540(1-e^{-0.1x})	\frac{d}{dx}(540(1-e^{-0.1x}))
sum from n=3 to infinity of 2/(n^2+1)	\sum\:_{n=3}^{\infty\:}\frac{2}{n^{2}+1}
integral of ((ln^3(x)))/x	\int\:\frac{(\ln^{3}(x))}{x}dx
2y^'-y=e^{t/3}	2y^{\prime\:}-y=e^{\frac{t}{3}}
derivative of f(x)=5ln(x)	derivative\:f(x)=5\ln(x)
integral from 0 to 2 of-2x^3sqrt(x^2+4)	\int\:_{0}^{2}-2x^{3}\sqrt{x^{2}+4}dx
limit as x approaches 3-of (\|x-3\|)/(x+3)	\lim\:_{x\to\:3-}(\frac{\left\|x-3\right\|}{x+3})
slope of 3t-t^2(0)	slope\:3t-t^{2}(0)
d/(dt)(5te^{-t})	\frac{d}{dt}(5te^{-t})
(\partial)/(\partial y)(((x^2))/((x-y)^2))	\frac{\partial\:}{\partial\:y}(\frac{(x^{2})}{(x-y)^{2}})
limit as x approaches 2 of \sqrt[6]{2-x}	\lim\:_{x\to\:2}(\sqrt[6]{2-x})
(dy)/(dx)=(x-3)/(y+1)	\frac{dy}{dx}=\frac{x-3}{y+1}
integral of-x/(x^2+1)	\int\:-\frac{x}{x^{2}+1}dx
integral of 1/((x-2)^2(x^2-4x+3))	\int\:\frac{1}{(x-2)^{2}(x^{2}-4x+3)}dx
derivative of f(x)=x^3+4x^2+3x	derivative\:f(x)=x^{3}+4x^{2}+3x
integral of (9-x^2)/x	\int\:\frac{9-x^{2}}{x}dx
derivative of (x-1(x^2+2)^3)	\frac{d}{dx}((x-1)(x^{2}+2)^{3})
(\partial)/(\partial x)(ln(2+x^2y^2))	\frac{\partial\:}{\partial\:x}(\ln(2+x^{2}y^{2}))
integral of (6x^3)/(sqrt(x^2+9))	\int\:\frac{6x^{3}}{\sqrt{x^{2}+9}}dx
limit as t approaches-1 of t^2-1	\lim\:_{t\to\:-1}(t^{2}-1)
integral of sin(5x)*cos(2x)	\int\:\sin(5x)\cdot\:\cos(2x)dx
derivative of f(t)=ln(t^9+5)	derivative\:f(t)=\ln(t^{9}+5)
tangent of y=4x-x^2,(1,3)	tangent\:y=4x-x^{2},(1,3)
(dy)/(dx)+8y=10	\frac{dy}{dx}+8y=10
tangent of f(x)=3x-4x^2,(-3,-45)	tangent\:f(x)=3x-4x^{2},(-3,-45)
derivative of (x-3^3(2x-1)^2)	\frac{d}{dx}((x-3)^{3}(2x-1)^{2})
derivative of (\sqrt[3]{x^2+3})/x	derivative\:\frac{\sqrt[3]{x^{2}+3}}{x}
f^'(x)=sin(4)(4x^5)	f^{\prime\:}(x)=\sin(4)(4x^{5})
derivative of 9(x-4)^{2/3}	derivative\:9(x-4)^{\frac{2}{3}}
derivative of 210	\frac{d}{dx}(210)
derivative of (e^{-x^2}/(x^3))	\frac{d}{dx}(\frac{e^{-x^{2}}}{x^{3}})
derivative of ln(6-x^2+2x^4)	derivative\:\ln(6-x^{2}+2x^{4})
integral from 1 to infinity of 7/(x^2+1)	\int\:_{1}^{\infty\:}\frac{7}{x^{2}+1}dx
derivative of y=(((x^2-2)/(2x^2+1))^2)	derivative\:y=((\frac{x^{2}-2}{2x^{2}+1})^{2})
integral of sqrt(6)	\int\:\sqrt{6}dx
derivative of \|2x-1\|	\frac{d}{dx}(\left\|2x-1\right\|)
(\partial)/(\partial x)(((x-y))/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{(x-y)}{x+y})
derivative of (x-1^{-2})	\frac{d}{dx}((x-1)^{-2})
y^'+3y=4e^{-t}	y^{\prime\:}+3y=4e^{-t}
limit as x approaches 10-of 1/(x-10)	\lim\:_{x\to\:10-}(\frac{1}{x-10})
integral from-1 to 1 of (3x)/((x+5)^2)	\int\:_{-1}^{1}\frac{3x}{(x+5)^{2}}dx
tangent of f(x)=-x^2-4x-6,\at x=4	tangent\:f(x)=-x^{2}-4x-6,\at\:x=4
integral of cos((pit)/2)	\int\:\cos(\frac{πt}{2})dt
derivative of \sqrt[3]{10+13pi}	\frac{d}{dx}(\sqrt[3]{10+13π})
integral of (tan^3(ln(x)))/(8x)	\int\:\frac{\tan^{3}(\ln(x))}{8x}dx
(d^2)/(dx^2)y=sin(x)	\frac{d^{2}}{dx^{2}}y=\sin(x)
integral of (2x^3)	\int\:(2x^{3})dx
y^'+2y=5	y^{\prime\:}+2y=5
tangent of (3x)/((2-3x)^3),\at x=2	tangent\:\frac{3x}{(2-3x)^{3}},\at\:x=2
integral from 1 to 3 of 3x^2	\int\:_{1}^{3}3x^{2}dx
xy^'+3y=((2e^{-4x}))/(x^2)	xy^{\prime\:}+3y=\frac{(2e^{-4x})}{x^{2}}
derivative of y(1+e^x)	\frac{d}{dx}(y(1+e^{x}))
limit as x approaches 1 of 0.99^{2-1}	\lim\:_{x\to\:1}(0.99^{2-1})
derivative of-(13/(x^5))	\frac{d}{dx}(-\frac{13}{x^{5}})
(\partial)/(\partial y)(-sin(x))	\frac{\partial\:}{\partial\:y}(-\sin(x))
derivative of 3xarcsin(x)	derivative\:3x\arcsin(x)
derivative of (2(3x^4-5)/(x^3))	\frac{d}{dx}(\frac{2(3x^{4}-5)}{x^{3}})
slope ofintercept (-2.2)(0)	slopeintercept\:(-2.2)(0)
area y=6x^2,y=x^2+4	area\:y=6x^{2},y=x^{2}+4
derivative of sqrt(3+x^2)	\frac{d}{dx}(\sqrt{3+x^{2}})
(\partial)/(\partial y)(arctan(x))	\frac{\partial\:}{\partial\:y}(\arctan(x))
derivative of 2(x-2pi)	\frac{d}{dx}(2(x-2π))

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