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Popular Calculus Problems

f^'(x)=x(x-3)	f^{\prime\:}(x)=x(x-3)
roots 3xy^2	roots\:3xy^{2}
(\partial)/(\partial z)(ln(sqrt(x^2+y^2+z^2)))	\frac{\partial\:}{\partial\:z}(\ln(\sqrt{x^{2}+y^{2}+z^{2}}))
(\partial)/(\partial y)(e^ycos(x))	\frac{\partial\:}{\partial\:y}(e^{y}\cos(x))
limit as x approaches 0 of e^{x+1}	\lim\:_{x\to\:0}(e^{x+1})
integral of cos(t-2x)	\int\:\cos(t-2x)dx
integral of (6x^2-3x)	\int\:(6x^{2}-3x)dx
derivative of log_{6}(2x^3-5x^2)	\frac{d}{dx}(\log_{6}(2x^{3}-5x^{2}))
integral of tan^2(xse)c^3x	\int\:\tan^{2}(xse)c^{3}xdx
derivative of (1+x^{15})	\frac{d}{dx}((1+x)^{15})
y^{''}+4y=sin(2t)	y^{\prime\:\prime\:}+4y=\sin(2t)
integral from 0 to 2 of 7^{-x}	\int\:_{0}^{2}7^{-x}dx
integral of-10x	\int\:-10xdx
integral from 2 to 5 of (x-4)^2	\int\:_{2}^{5}(x-4)^{2}dx
derivative of (tan(x-x)/(x^3))	\frac{d}{dx}(\frac{\tan(x)-x}{x^{3}})
integral of x^3sqrt(x^2+18)	\int\:x^{3}\sqrt{x^{2}+18}dx
limit as x approaches 4 of (x-4)/(\|x-4\|)	\lim\:_{x\to\:4}(\frac{x-4}{\left\|x-4\right\|})
derivative of 2cos(cot(2x+1))	\frac{d}{dx}(2\cos(\cot(2x+1)))
limit as x approaches-7+of sqrt(1/(x+7))	\lim\:_{x\to\:-7+}(\sqrt{\frac{1}{x+7}})
integral from 2 to 4 of 3e^{3x}	\int\:_{2}^{4}3e^{3x}dx
derivative of 6e^x	\frac{d}{dx}(6e^{x})
limit as x approaches 1 of 3x+1	\lim\:_{x\to\:1}(3x+1)
integral of x(ln(x))^3	\int\:x(\ln(x))^{3}dx
integral of (e^{3x})/(1+e^x)	\int\:\frac{e^{3x}}{1+e^{x}}dx
limit as x approaches 3 of x^2+3x-1	\lim\:_{x\to\:3}(x^{2}+3x-1)
integral of e^2cos(3x)	\int\:e^{2}\cos(3x)dx
derivative of cos(arcsin(3x))	\frac{d}{dx}(\cos(\arcsin(3x)))
(dx)/(dt)=6-(7x)/(600+2t)	\frac{dx}{dt}=6-\frac{7x}{600+2t}
integral of (3sqrt(x)-5)/(x^2)	\int\:\frac{3\sqrt{x}-5}{x^{2}}dx
integral of (x^3+23)/(x^2+7x+12)	\int\:\frac{x^{3}+23}{x^{2}+7x+12}dx
derivative of (2x+1^4)	\frac{d}{dx}((2x+1)^{4})
derivative of y=csc(x)(x+cot(x))	derivative\:y=\csc(x)(x+\cot(x))
derivative of f(x)=(2x)/(7x^2+1)	derivative\:f(x)=\frac{2x}{7x^{2}+1}
integral of 7^xcot^2(7^x)	\int\:7^{x}\cot^{2}(7^{x})dx
x^6+y^5sqrt(x^7+4)(dy)/(dx)=0	x^{6}+y^{5}\sqrt{x^{7}+4}\frac{dy}{dx}=0
(dy)/(dx)=-(2xy)/(x^2+36)	\frac{dy}{dx}=-\frac{2xy}{x^{2}+36}
derivative of arcsec(18x)	\frac{d}{dx}(\arcsec(18x))
integral of 4/(x(ln(x))^3)	\int\:\frac{4}{x(\ln(x))^{3}}dx
integral of t/(1+t)	\int\:\frac{t}{1+t}dt
implicit 6x^2+3y^2=12	implicit\:6x^{2}+3y^{2}=12
integral of (x^3-1/(x^3))(x^3+1/(x^3))	\int\:(x^{3}-\frac{1}{x^{3}})(x^{3}+\frac{1}{x^{3}})dx
d/(du)(u^2v)	\frac{d}{du}(u^{2}v)
integral of sin(x/2)cos((2x)/3)	\int\:\sin(\frac{x}{2})\cos(\frac{2x}{3})dx
derivative of 81m^8+2m^4+1	derivative\:81m^{8}+2m^{4}+1
derivative of arcsin(4x+1)	derivative\:\arcsin(4x+1)
derivative of x/(2x^2+1)	\frac{d}{dx}(\frac{x}{2x^{2}+1})
integral of (7+x^5)^65x^4	\int\:(7+x^{5})^{6}5x^{4}dx
derivative of cos(1/2 x)	\frac{d}{dx}(\cos(\frac{1}{2}x))
y^{''}-16y^'+64y=8t^6e^{8t}	y^{\prime\:\prime\:}-16y^{\prime\:}+64y=8t^{6}e^{8t}
derivative of sqrt(x^2+17)	\frac{d}{dx}(\sqrt{x^{2}+17})
derivative of 2ln(x+3)	\frac{d}{dx}(2\ln(x)+3)
integral of (x^{20}-5x^4)^5(x^{19}-x^3)	\int\:(x^{20}-5x^{4})^{5}(x^{19}-x^{3})dx
integral of (3x+27)/((2x-2)(x+5))	\int\:\frac{3x+27}{(2x-2)(x+5)}dx
area y= 2/x ,y= 1/2 x,y=8x	area\:y=\frac{2}{x},y=\frac{1}{2}x,y=8x
derivative of u^{3/2}(u+ce^u)	derivative\:u^{\frac{3}{2}}(u+ce^{u})
integral from 1 to infinity of 3/(x^3)	\int\:_{1}^{\infty\:}\frac{3}{x^{3}}dx
(\partial)/(\partial x)(x^3-x^2+y^3-y^2)	\frac{\partial\:}{\partial\:x}(x^{3}-x^{2}+y^{3}-y^{2})
integral of xe^{x^2-1}	\int\:xe^{x^{2}-1}dx
integral from 0 to 1 of e^{x^4}	\int\:_{0}^{1}e^{x^{4}}dx
integral of cos^4(xta)n^3x	\int\:\cos^{4}(xta)n^{3}xdx
taylor e^{-h}	taylor\:e^{-h}
slope of (-2,-7),(2,-1)	slope\:(-2,-7),(2,-1)
integral of ((sec^2(x)))/(tan(x))	\int\:\frac{(\sec^{2}(x))}{\tan(x)}dx
d/(dy)(1/(y(1-xy)))	\frac{d}{dy}(\frac{1}{y(1-xy)})
integral of ((x^2))/((15+4x-4x^2)^{3/2)}	\int\:\frac{(x^{2})}{(15+4x-4x^{2})^{\frac{3}{2}}}dx
integral from-1 to 8 of 1/(\sqrt[3]{x)}	\int\:_{-1}^{8}\frac{1}{\sqrt[3]{x}}dx
integral of 3/(x^2+x-2)	\int\:\frac{3}{x^{2}+x-2}dx
integral of sqrt((3t^2)^2+(2t)^2)	\int\:\sqrt{(3t^{2})^{2}+(2t)^{2}}dt
integral of (arccos(x))/(sqrt(1-x^2))	\int\:\frac{\arccos(x)}{\sqrt{1-x^{2}}}dx
integral of t(t^3-1)	\int\:t(t^{3}-1)dt
derivative of (e^x+cos(x)/(x^2))	\frac{d}{dx}(\frac{e^{x}+\cos(x)}{x^{2}})
3y^'=2y	3y^{\prime\:}=2y
integral of (x^2)/(sqrt(25+x^2))	\int\:\frac{x^{2}}{\sqrt{25+x^{2}}}dx
derivative of 7x^4-2x^3+8x+5	\frac{d}{dx}(7x^{4}-2x^{3}+8x+5)
limit as x approaches 0 of e^{2x}-1	\lim\:_{x\to\:0}(e^{2x}-1)
integral of (x+1)e^{4x+1}	\int\:(x+1)e^{4x+1}dx
y^'+2y= 6/5	y^{\prime\:}+2y=\frac{6}{5}
derivative of y=8(x+2)^{3/2}	derivative\:y=8(x+2)^{\frac{3}{2}}
integral of (5e^{2x})/(e^{2x)+13e^x+36}	\int\:\frac{5e^{2x}}{e^{2x}+13e^{x}+36}dx
integral from 0 to 1 of pi(x^3)^2	\int\:_{0}^{1}π(x^{3})^{2}dx
integral of ye^{-x^2}	\int\:ye^{-x^{2}}dx
slope of (-5,-3),(5,2)	slope\:(-5,-3),(5,2)
integral from 0 to 2pi of 2a(sin(t/2))	\int\:_{0}^{2π}2a(\sin(\frac{t}{2}))dt
sum from n=1 to infinity of n^2*x^n	\sum\:_{n=1}^{\infty\:}n^{2}\cdot\:x^{n}
derivative of \sqrt[4]{2x^{12}+sin(4x)}	derivative\:\sqrt[4]{2x^{12}+\sin(4x)}
derivative of-(12x/((x^2+3)^2))	\frac{d}{dx}(-\frac{12x}{(x^{2}+3)^{2}})
(\partial)/(\partial x)((xy)/(sqrt(x^2+9)))	\frac{\partial\:}{\partial\:x}(\frac{xy}{\sqrt{x^{2}+9}})
integral of 8sqrt(36-4x)-32	\int\:8\sqrt{36-4x}-32dx
integral of (4+5x)/(1+x^2)	\int\:\frac{4+5x}{1+x^{2}}dx
d/(dt)((90cos(pi/6))t)	\frac{d}{dt}((90\cos(\frac{π}{6}))t)
integral of (ln(21x))/x	\int\:\frac{\ln(21x)}{x}dx
derivative of x/(9x+2)	\frac{d}{dx}(\frac{x}{9x+2})
integral of (9-5x)	\int\:(9-5x)dx
(\partial)/(\partial x)(2x-6y^2-6)	\frac{\partial\:}{\partial\:x}(2x-6y^{2}-6)
integral of sec^2(2x)	\int\:\sec^{2}(2x)dx
f(x)=x^5ln(x)	f(x)=x^{5}\ln(x)
integral of e^{2x^2+4}	\int\:e^{2x^{2}+4}dx
(dy)/(dx)= 1/(2x(7-x))	\frac{dy}{dx}=\frac{1}{2x(7-x)}
y^'-3x^2y=12x^2	y^{\prime\:}-3x^{2}y=12x^{2}
derivative of (5x^2-8x)e^x	derivative\:(5x^{2}-8x)e^{x}

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