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Popular Calculus Problems

integral of (2x)/1	\int\:\frac{2x}{1}dx
sum from n=0 to infinity of 1.02^n	\sum\:_{n=0}^{\infty\:}1.02^{n}
slope ofintercept (3,-3),(0,2)	slopeintercept\:(3,-3),(0,2)
integral of (x^3-3x^2+4x-9)/(x^2+3)	\int\:\frac{x^{3}-3x^{2}+4x-9}{x^{2}+3}dx
derivative of-cos(2x)	derivative\:-\cos(2x)
integral from 1 to 4 of (x-2)/(sqrt(x))	\int\:_{1}^{4}\frac{x-2}{\sqrt{x}}dx
derivative of f(x)=3arccsc(x)	derivative\:f(x)=3\arccsc(x)
integral of x^2sech^2(x^3)	\int\:x^{2}\sech^{2}(x^{3})dx
derivative of sqrt(x^3-8)	\frac{d}{dx}(\sqrt{x^{3}-8})
y^'+2y=25sin(x)+40cos(x),y(0)=1	y^{\prime\:}+2y=25\sin(x)+40\cos(x),y(0)=1
tangent of y=sqrt(x),(9,3)	tangent\:y=\sqrt{x},(9,3)
sum from n=6 to infinity of (5^n)/(12^n)	\sum\:_{n=6}^{\infty\:}\frac{5^{n}}{12^{n}}
3y^{''}+17y^'-6y=0	3y^{\prime\:\prime\:}+17y^{\prime\:}-6y=0
derivative of 1/(x^4+1/(x^2)-x^3)	\frac{d}{dx}(\frac{1}{x^{4}}+\frac{1}{x^{2}}-x^{3})
integral of (x^2-5)^5*2x	\int\:(x^{2}-5)^{5}\cdot\:2xdx
y^{''}=xe^x	y^{\prime\:\prime\:}=xe^{x}
tangent of f(x)=x^3-2x^2+4x+3,\at x=1	tangent\:f(x)=x^{3}-2x^{2}+4x+3,\at\:x=1
10x-8y*sqrt(x^2+1)(dy)/(dx)=0,y(0)=4	10x-8y\cdot\:\sqrt{x^{2}+1}\frac{dy}{dx}=0,y(0)=4
derivative of f(x)=((x-5))/((x+3)^4)	derivative\:f(x)=\frac{(x-5)}{(x+3)^{4}}
integral from 0 to 1 of-12e^x	\int\:_{0}^{1}-12e^{x}dx
derivative of x^6e^{-x}	\frac{d}{dx}(x^{6}e^{-x})
taylor ln(x),6	taylor\:\ln(x),6
derivative of 8+3sin(x)	\frac{d}{dx}(8+3\sin(x))
integral from 0 to 1 of x^{1/2}	\int\:_{0}^{1}x^{\frac{1}{2}}dx
sum from n=1 to infinity of 1/(2^nn!)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}n!}
xy^'+y=37sqrt(x)	xy^{\prime\:}+y=37\sqrt{x}
derivative of 1/3*\sqrt[3]{x}	\frac{d}{dx}(\frac{1}{3}\cdot\:\sqrt[3]{x})
limit as x approaches 0 of (4^x-10^x)/x	\lim\:_{x\to\:0}(\frac{4^{x}-10^{x}}{x})
d/(dt)(1+cos(t))	\frac{d}{dt}(1+\cos(t))
-2y^'+(4y)/x =(y^3)/x	-2y^{\prime\:}+\frac{4y}{x}=\frac{y^{3}}{x}
d/(dt)(1/(t^2))	\frac{d}{dt}(\frac{1}{t^{2}})
integral of (5x-1)/((2x+1)(x-1))	\int\:\frac{5x-1}{(2x+1)(x-1)}dx
f(x)=arctan(3x)	f(x)=\arctan(3x)
(dy)/(dt)=ky(100-y)	\frac{dy}{dt}=ky(100-y)
derivative of log_{4}((x^2+2x^3))	\frac{d}{dx}(\log_{4}((x^{2}+2x)^{3}))
f(x)=xsqrt(8-x^2)	f(x)=x\sqrt{8-x^{2}}
integral of (1+cos(y))	\int\:(1+\cos(y))dy
taylor pi/6 cos(x)	taylor\:\frac{π}{6}\cos(x)
derivative of 2-x^6	derivative\:2-x^{6}
integral of 5x-x^2-x	\int\:5x-x^{2}-xdx
limit as h approaches 0 of ((4+h)-(4))/h	\lim\:_{h\to\:0}(\frac{(4+h)-(4)}{h})
x(dy)/(dx)-2y=x^{-2}+2x^3e^x	x\frac{dy}{dx}-2y=x^{-2}+2x^{3}e^{x}
integral of (e^x)/(5+e^{2x)}	\int\:\frac{e^{x}}{5+e^{2x}}dx
derivative of 1/2 (sin(x+xcos(x)))	\frac{d}{dx}(\frac{1}{2}(\sin(x)+x\cos(x)))
derivative of cot(3x^2-8)	\frac{d}{dx}(\cot(3x^{2}-8))
limit as x approaches 5 of e^6	\lim\:_{x\to\:5}(e^{6})
sum from n=0 to infinity of 1/((2n+1)^2)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n+1)^{2}}
derivative of sqrt(7-x^2)	\frac{d}{dx}(\sqrt{7-x^{2}})
limit as x approaches pi of-6sin(x)+4x	\lim\:_{x\to\:π}(-6\sin(x)+4x)
t((dy)/(dt))+27y= 1/t	t(\frac{dy}{dt})+27y=\frac{1}{t}
(\partial)/(\partial θ)(tan(θ))	\frac{\partial\:}{\partial\:θ}(\tan(θ))
taylor f(x)=e^x	taylor\:f(x)=e^{x}
(dq)/(dt)+3*q=0,q(0)=9	\frac{dq}{dt}+3\cdot\:q=0,q(0)=9
limit as x approaches 0 of x[x]	\lim\:_{x\to\:0}(x[x])
derivative of f(x)=-2/(x^2)	derivative\:f(x)=-\frac{2}{x^{2}}
integral of sin^3(13x)	\int\:\sin^{3}(13x)dx
tangent of f(x)=x^3+6x^2+19x+15,\at x=7	tangent\:f(x)=x^{3}+6x^{2}+19x+15,\at\:x=7
derivative of y=10sqrt(x)	derivative\:y=10\sqrt{x}
derivative of 6e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(6e^{x}+\frac{2}{\sqrt[3]{x}})
(3t^2)^'	(3t^{2})^{\prime\:}
implicit (dy)/(dx),y=4^x	implicit\:\frac{dy}{dx},y=4^{x}
derivative of ln(x^2+14x+55)	\frac{d}{dx}(\ln(x^{2}+14x+55))
derivative of (4t)/(4+sqrt(t))	derivative\:\frac{4t}{4+\sqrt{t}}
limit as x approaches 4 of sqrt(x+4)	\lim\:_{x\to\:4}(\sqrt{x+4})
integral of-2xln(x)	\int\:-2x\ln(x)dx
integral of-2x^3	\int\:-2x^{3}dx
derivative of 2arctan(sqrt(x))	\frac{d}{dx}(2\arctan(\sqrt{x}))
(\partial}{\partial x}(\frac{x^2)/2+(y^3)/3)	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{2}+\frac{y^{3}}{3})
derivative of f(x)=5ex	derivative\:f(x)=5ex
d/(dt)(t^{1/2})	\frac{d}{dt}(t^{\frac{1}{2}})
limit as x approaches 0 of ((3+x^2)-9)/x	\lim\:_{x\to\:0}(\frac{(3+x^{2})-9}{x})
derivative of (2x^2+x+9^{-3})	\frac{d}{dx}((2x^{2}+x+9)^{-3})
integral of (1-x^2)/(x+x^3)	\int\:\frac{1-x^{2}}{x+x^{3}}dx
derivative of 5x^3+7x^{2.5}-3x+1	\frac{d}{dx}(5x^{3}+7x^{2.5}-3x+1)
limit as x approaches 0 of (7x^2-2x)/x	\lim\:_{x\to\:0}(\frac{7x^{2}-2x}{x})
integral of (4/x+x/4)	\int\:(\frac{4}{x}+\frac{x}{4})dx
derivative of 11xe^x	derivative\:11xe^{x}
(\partial)/(\partial y)(5xy)	\frac{\partial\:}{\partial\:y}(5xy)
derivative of (sin(2x)/(sin(3x)))	\frac{d}{dx}(\frac{\sin(2x)}{\sin(3x)})
ln(x)(dy)/(dx)= y/x	\ln(x)\frac{dy}{dx}=\frac{y}{x}
(\partial)/(\partial y)(e^x+xcos(y))	\frac{\partial\:}{\partial\:y}(e^{x}+x\cos(y))
25y^{''}-4y=0	25y^{\prime\:\prime\:}-4y=0
derivative of e^{3k}	derivative\:e^{3k}
derivative of (3x^4+4x^2(5x+8)^4)	\frac{d}{dx}((3x^{4}+4x)^{2}(5x+8)^{4})
limit as t approaches 0 of (e^{6t}-1)/t	\lim\:_{t\to\:0}(\frac{e^{6t}-1}{t})
derivative of y=-4e^{-4x}	derivative\:y=-4e^{-4x}
integral of 7cos(x)	\int\:7\cos(x)dx
integral from 0 to 1 of (2^x)/(2^x+2)	\int\:_{0}^{1}\frac{2^{x}}{2^{x}+2}dx
integral of tan^3(x/2)sec^2(x/2)	\int\:\tan^{3}(\frac{x}{2})\sec^{2}(\frac{x}{2})dx
derivative of tan(x+y)	\frac{d}{dx}(\tan(x+y))
derivative of ((5-x^{-2})/2)	\frac{d}{dx}(\frac{(5-x)^{-2}}{2})
derivative of 0.2x^2	\frac{d}{dx}(0.2x^{2})
(d^2)/(dx^2)(14x^3-36x^2)	\frac{d^{2}}{dx^{2}}(14x^{3}-36x^{2})
(dQ)/(dt)= 12/5-3Q	\frac{dQ}{dt}=\frac{12}{5}-3Q
derivative of 1+sqrt(3x)	\frac{d}{dx}(1+\sqrt{3x})
(\partial)/(\partial y)(xln(1+x+y))	\frac{\partial\:}{\partial\:y}(x\ln(1+x+y))
integral of 8xcos(4x)	\int\:8x\cos(4x)dx
integral from 0 to 1 of 2pix(3e^{-x^2})	\int\:_{0}^{1}2πx(3e^{-x^{2}})dx
limit as x approaches 2 of 2/((x-2)^5)	\lim\:_{x\to\:2}(\frac{2}{(x-2)^{5}})
integral of ((ln(x))^2)/(x^2)	\int\:\frac{(\ln(x))^{2}}{x^{2}}dx

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