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Popular Calculus Problems

slope of f(x)=x^2+x-3	slope\:f(x)=x^{2}+x-3
3t^4y^{''}+7t^3y^'=0	3t^{4}y^{\prime\:\prime\:}+7t^{3}y^{\prime\:}=0
sum from n=0 to infinity of 1/((n+10))	\sum\:_{n=0}^{\infty\:}\frac{1}{(n+10)}
integral of 14tan^3(x)	\int\:14\tan^{3}(x)dx
y^{''}-2y+y=0	y^{\prime\:\prime\:}-2y+y=0
integral from-4 to 6 of f(x)	\int\:_{-4}^{6}f(x)dx
limit as x approaches 0 of (ln(x))/1	\lim\:_{x\to\:0}(\frac{\ln(x)}{1})
y^'-9xy=0	y^{\prime\:}-9xy=0
derivative of f(x)=3253(86.3)^x	derivative\:f(x)=3253(86.3)^{x}
(\partial)/(\partial x)(xln(y)-yln(x))	\frac{\partial\:}{\partial\:x}(x\ln(y)-y\ln(x))
limit as n approaches infinity of n/5	\lim\:_{n\to\:\infty\:}(\frac{n}{5})
limit as x approaches 5 of 12	\lim\:_{x\to\:5}(12)
derivative of x^4+2/x	\frac{d}{dx}(x^{4}+\frac{2}{x})
derivative of 3x^2+2x+4	\frac{d}{dx}(3x^{2}+2x+4)
integral from 0 to 2 of 1/(x^{1/3)}	\int\:_{0}^{2}\frac{1}{x^{\frac{1}{3}}}dx
(sqrt(x^3))^'	(\sqrt{x^{3}})^{\prime\:}
f(x)=sqrt(x-3)	f(x)=\sqrt{x-3}
integral of 2x^6	\int\:2x^{6}dx
integral of e^2xcos(3x)	\int\:e^{2}x\cos(3x)dx
integral of x^3e^{x^2}	\int\:x^{3}e^{x^{2}}dx
(\partial)/(\partial x)(sin(xyz^3))	\frac{\partial\:}{\partial\:x}(\sin(xyz^{3}))
integral from 0 to 5 of e^{3x}	\int\:_{0}^{5}e^{3x}dx
4y^{''}-16y^'+19y=0	4y^{\prime\:\prime\:}-16y^{\prime\:}+19y=0
derivative of 2x^2cos(x)	\frac{d}{dx}(2x^{2}\cos(x))
(y^')/y =x	\frac{y^{\prime\:}}{y}=x
tangent of (6x)/(2+x^2)	tangent\:\frac{6x}{2+x^{2}}
(\partial)/(\partial y)(e^{2y}sin(-2x))	\frac{\partial\:}{\partial\:y}(e^{2y}\sin(-2x))
derivative of f(x)=(2x+3)^{11}(4-5x)^9	derivative\:f(x)=(2x+3)^{11}(4-5x)^{9}
limit as x approaches 1+of 1	\lim\:_{x\to\:1+}(1)
9/10 x^2dy-18dx=0	\frac{9}{10}x^{2}dy-18dx=0
(\partial)/(\partial x)(x^3+x^2y-y^2-4y)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}y-y^{2}-4y)
derivative of 4x+5	\frac{d}{dx}(4x+5)
limit as x approaches 5+of 2/(x+5)	\lim\:_{x\to\:5+}(\frac{2}{x+5})
(\partial)/(\partial x)(ax+by^2+cx^2y)	\frac{\partial\:}{\partial\:x}(ax+by^{2}+cx^{2}y)
derivative of arctan(tan(x))	\frac{d}{dx}(\arctan(\tan(x)))
limit as x approaches 0+of xln(x^2)	\lim\:_{x\to\:0+}(x\ln(x^{2}))
area y=9-x^2,y=0,x	area\:y=9-x^{2},y=0,x
derivative of ((3x-1)/(x^{2/3)})	\frac{d}{dx}(\frac{(3x-1)}{x^{\frac{2}{3}}})
(\partial)/(\partial x)(4+xln(xy-5))	\frac{\partial\:}{\partial\:x}(4+x\ln(xy-5))
derivative of x(2-x)	\frac{d}{dx}(x(2-x))
integral of (5x)/(e^{2x)}	\int\:\frac{5x}{e^{2x}}dx
integral of (7x+8)/(7x^2+16x+9)	\int\:\frac{7x+8}{7x^{2}+16x+9}dx
derivative of 1/(x^{11})	\frac{d}{dx}(\frac{1}{x^{11}})
limit as x approaches 3+of (18-6x)/(3-x)	\lim\:_{x\to\:3+}(\frac{18-6x}{3-x})
derivative of 2\sqrt[3]{x^7}	\frac{d}{dx}(2\sqrt[3]{x^{7}})
integral of x^2-8x+12	\int\:x^{2}-8x+12dx
derivative of ln(x+sqrt(1-x^2))	\frac{d}{dx}(\ln(x+\sqrt{1-x^{2}}))
sum from n=0 to infinity of (5/4)(2/3)^n	\sum\:_{n=0}^{\infty\:}(\frac{5}{4})(\frac{2}{3})^{n}
sum from n=0 to infinity of n/(n^2+2)	\sum\:_{n=0}^{\infty\:}\frac{n}{n^{2}+2}
integral of ((x^2)/2-2/(x^2))	\int\:(\frac{x^{2}}{2}-\frac{2}{x^{2}})dx
(\partial)/(\partial x)((3y)/(x^2+2))	\frac{\partial\:}{\partial\:x}(\frac{3y}{x^{2}+2})
derivative of 3/4 x^{4/3}-3/8 x^{2/3}	\frac{d}{dx}(\frac{3}{4}x^{\frac{4}{3}}-\frac{3}{8}x^{\frac{2}{3}})
tangent of x-x^3	tangent\:x-x^{3}
derivative of x/((1+x))	\frac{d}{dx}(\frac{x}{(1+x)})
integral of (x^2+3x+2)/(x^2(x+3))	\int\:\frac{x^{2}+3x+2}{x^{2}(x+3)}dx
integral of (a^{sqrt(t)})/(sqrt(t))	\int\:\frac{a^{\sqrt{t}}}{\sqrt{t}}dt
integral of 6sin^3(x)cos^5(x)	\int\:6\sin^{3}(x)\cos^{5}(x)dx
(x^x)^'	(x^{x})^{\prime\:}
limit as x approaches 2-of ln(4-2x)	\lim\:_{x\to\:2-}(\ln(4-2x))
integral of tan^2(t)sec^3(t)	\int\:\tan^{2}(t)\sec^{3}(t)dt
sum from n=0 to infinity of 5^{-n}	\sum\:_{n=0}^{\infty\:}5^{-n}
derivative of ln(1+8x)	\frac{d}{dx}(\ln(1+8x))
limit as x approaches 1+of 1/(x^2+1)	\lim\:_{x\to\:1+}(\frac{1}{x^{2}+1})
(\partial)/(\partial y)(e^{xe^y})	\frac{\partial\:}{\partial\:y}(e^{xe^{y}})
integral of (1-y^2)	\int\:(1-y^{2})dy
y^{''}+7y^'+10y=-18te^{2t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=-18te^{2t}
limit as x approaches 0 of 0/(sqrt(x^2))	\lim\:_{x\to\:0}(\frac{0}{\sqrt{x^{2}}})
derivative of (0.9e^x)/(tan(x))	derivative\:\frac{0.9e^{x}}{\tan(x)}
integral from 6 to 8 of 6/((x-6)^3)	\int\:_{6}^{8}\frac{6}{(x-6)^{3}}dx
derivative of (x^3+1/(x^2+3))	\frac{d}{dx}(\frac{x^{3}+1}{x^{2}+3})
derivative of (sin(x)+2tan(x))(sec(x)-3csc(x))	derivative\:(\sin(x)+2\tan(x))(\sec(x)-3\csc(x))
derivative of 1/(x^{12})	\frac{d}{dx}(\frac{1}{x^{12}})
derivative of tan(2x^2-x+3)	derivative\:\tan(2x^{2}-x+3)
derivative of y=9sec(1/3 x)	derivative\:y=9\sec(\frac{1}{3}x)
f(x)=2xln(x)+x	f(x)=2x\ln(x)+x
integral of ((5-10x^2)/(4x^3-6x+15))	\int\:(\frac{5-10x^{2}}{4x^{3}-6x+15})dx
derivative of f(x)=xsqrt(x^2+21)	derivative\:f(x)=x\sqrt{x^{2}+21}
limit as x approaches infinity of 1+4x	\lim\:_{x\to\:\infty\:}(1+4x)
x^2(dy)/(dx)-xy+1=0	x^{2}\frac{dy}{dx}-xy+1=0
limit as x approaches infinity of-x/x	\lim\:_{x\to\:\infty\:}(-\frac{x}{x})
integral from 0 to 3 of 2e^x	\int\:_{0}^{3}2e^{x}dx
derivative of ln(x-(x^2)/8)	\frac{d}{dx}(\ln(x)-\frac{x^{2}}{8})
limit as x approaches-3 of (x-5)(x+4)	\lim\:_{x\to\:-3}((x-5)(x+4))
integral from 0 to infinity of 1/(4+x)	\int\:_{0}^{\infty\:}\frac{1}{4+x}dx
limit as x approaches 0 of x/(1-(x-1)^2)	\lim\:_{x\to\:0}(\frac{x}{1-(x-1)^{2}})
limit as t approaches 0+of arctan(ln(t))	\lim\:_{t\to\:0+}(\arctan(\ln(t)))
taylor 9/x ,1	taylor\:\frac{9}{x},1
integral of (2x)/(sqrt(x^4+25))	\int\:\frac{2x}{\sqrt{x^{4}+25}}dx
derivative of ln(1+3/x+5/(x^2))	derivative\:\ln(1+\frac{3}{x}+\frac{5}{x^{2}})
integral of (x^4+3)^{3/2}x^3	\int\:(x^{4}+3)^{\frac{3}{2}}x^{3}dx
(\partial)/(\partial b)(mx^b)	\frac{\partial\:}{\partial\:b}(mx^{b})
integral of 8y	\int\:8ydy
integral of 4sin(4x)sin(3x)cos(2x)	\int\:4\sin(4x)\sin(3x)\cos(2x)dx
(\partial)/(\partial x)(e^{-3y}cos(3x))	\frac{\partial\:}{\partial\:x}(e^{-3y}\cos(3x))
limit as t approaches-infinity of e^t+1	\lim\:_{t\to\:-\infty\:}(e^{t}+1)
derivative of 0.01(0.2x^2+4x+64^{2/3})	\frac{d}{dx}(0.01(0.2x^{2}+4x+64)^{\frac{2}{3}})
integral from 0 to 10 of x^2e^{-0.08x}	\int\:_{0}^{10}x^{2}e^{-0.08x}dx
(\partial)/(\partial y)(y^5cos(3x))	\frac{\partial\:}{\partial\:y}(y^{5}\cos(3x))
integral of-x/2	\int\:-\frac{x}{2}dx
derivative of ((x^{1/3}-4))/(x^{7/2)}	derivative\:\frac{(x^{\frac{1}{3}}-4)}{x^{\frac{7}{2}}}

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