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Popular Calculus Problems

derivative of y^{-1}+y^{-2}	derivative\:y^{-1}+y^{-2}
integral from-1 to 0 of \|x^2-1\|	\int\:_{-1}^{0}\left\|x^{2}-1\right\|dx
limit as x approaches-9+of 1/(x+9)	\lim\:_{x\to\:-9+}(\frac{1}{x+9})
tangent of y=6x^2-x^3(1.5)	tangent\:y=6x^{2}-x^{3}(1.5)
limit as x approaches 0 of 1-x^2	\lim\:_{x\to\:0}(1-x^{2})
integral of x/((1+x)^2)	\int\:\frac{x}{(1+x)^{2}}dx
sqrt(x)+sqrt(y)y^'=0,y(1)=9	\sqrt{x}+\sqrt{y}y^{\prime\:}=0,y(1)=9
tangent of f(x)=2tan(x),\at x= pi/4	tangent\:f(x)=2\tan(x),\at\:x=\frac{π}{4}
derivative of sqrt(2x^2+2)	\frac{d}{dx}(\sqrt{2x^{2}+2})
(\partial)/(\partial y)((1+xy)e^{xy})	\frac{\partial\:}{\partial\:y}((1+xy)e^{xy})
sum from n=1 to infinity of (9^n)/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{9^{n}}{10^{n}}
integral of sec^3(8x)	\int\:\sec^{3}(8x)dx
integral of x^2sqrt(2x+5)	\int\:x^{2}\sqrt{2x+5}dx
tangent of y= 3/(sqrt(x)),(4, 3/2)	tangent\:y=\frac{3}{\sqrt{x}},(4,\frac{3}{2})
laplacetransform t^2cos(t)	laplacetransform\:t^{2}\cos(t)
y^{''}+4y^'+4y=t+e^{2t}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=t+e^{2t}
tangent of f(x)=9x^2	tangent\:f(x)=9x^{2}
integral of-2x^3+12x^2-20x+8.5	\int\:-2x^{3}+12x^{2}-20x+8.5dx
(dy)/(dx)+7xe^y=0	\frac{dy}{dx}+7xe^{y}=0
derivative of log_{4}(sec(x))	\frac{d}{dx}(\log_{4}(\sec(x)))
derivative of 3x^2-1/(x^2)	\frac{d}{dx}(3x^{2}-\frac{1}{x^{2}})
16y^{''}+8y^'+y=0	16y^{\prime\:\prime\:}+8y^{\prime\:}+y=0
integral from 1 to infinity of xe^{-10x}	\int\:_{1}^{\infty\:}xe^{-10x}dx
limit as x approaches 0 of (x+1)/(5x)	\lim\:_{x\to\:0}(\frac{x+1}{5x})
area x^2-2,7	area\:x^{2}-2,7
(d^2)/(dx^2)(arccos(3x))	\frac{d^{2}}{dx^{2}}(\arccos(3x))
integral of 1/(xln(x))	\int\:\frac{1}{x\ln(x)}dx
integral of (x^2)/(sqrt(x^2-25))	\int\:\frac{x^{2}}{\sqrt{x^{2}-25}}dx
integral of (1+y^2)/y	\int\:\frac{1+y^{2}}{y}dy
derivative of (x^3-x+1^{10})	\frac{d}{dx}((x^{3}-x+1)^{10})
tangent of y= 1/(x^4),(1,1)	tangent\:y=\frac{1}{x^{4}},(1,1)
integral of (x^6)/((3-x^7)^2)	\int\:\frac{x^{6}}{(3-x^{7})^{2}}dx
integral of (-6)/((x^2+6)^{3/2)}	\int\:\frac{-6}{(x^{2}+6)^{\frac{3}{2}}}dx
limit as x approaches 0+of (1+2/x)^x	\lim\:_{x\to\:0+}((1+\frac{2}{x})^{x})
derivative of 1+4x^3	\frac{d}{dx}(1+4x^{3})
integral of (1-2x)/(sqrt(x^2-4))	\int\:\frac{1-2x}{\sqrt{x^{2}-4}}dx
integral of tan^4(x)sec(x)	\int\:\tan^{4}(x)\sec(x)dx
integral from 2 to 7 of t^2ln(2t)	\int\:_{2}^{7}t^{2}\ln(2t)dt
integral of (tan(x))/(sec(x)+tan(x))	\int\:\frac{\tan(x)}{\sec(x)+\tan(x)}dx
integral of sin^2(x/5)	\int\:\sin^{2}(\frac{x}{5})dx
(dy)/(dt)=y+1+2sin(t)	\frac{dy}{dt}=y+1+2\sin(t)
(\partial)/(\partial z)(x^2ycos(z/t))	\frac{\partial\:}{\partial\:z}(x^{2}y\cos(\frac{z}{t}))
integral of sqrt(1-(x-1)^2)	\int\:\sqrt{1-(x-1)^{2}}dx
derivative of x^3-12x+1	\frac{d}{dx}(x^{3}-12x+1)
sum from n=1 to infinity of (-0.2)^n	\sum\:_{n=1}^{\infty\:}(-0.2)^{n}
laplacetransform 2cos(2t+pi/6)	laplacetransform\:2\cos(2t+\frac{π}{6})
lcm f(x)=,x\at x	lcm\:f(x)=,x\at\:x
derivative of f(x)=sqrt(x)+7	derivative\:f(x)=\sqrt{x}+7
limit as x approaches-3-of (x+2)/(x+3)	\lim\:_{x\to\:-3-}(\frac{x+2}{x+3})
integral of sqrt(2x-x^2)	\int\:\sqrt{2x-x^{2}}dx
tangent of y=50-x^2	tangent\:y=50-x^{2}
f(x)=3cos(x)	f(x)=3\cos(x)
limit as x approaches-5+of 1/(x^2-25)	\lim\:_{x\to\:-5+}(\frac{1}{x^{2}-25})
(t^2+2t)(dx)/(dt)=2x+6,x(1)=1	(t^{2}+2t)\frac{dx}{dt}=2x+6,x(1)=1
y^{''}+7y=0	y^{\prime\:\prime\:}+7y=0
derivative of e^{3x}+3xe^{3x}	\frac{d}{dx}(e^{3x}+3xe^{3x})
derivative of 2x^{4+7x+5}	\frac{d}{dx}(2x^{4+7x+5})
integral of y/((1+y^2))	\int\:\frac{y}{(1+y^{2})}dy
integral of (4x^2-3x+4)/(x^3+4x)	\int\:\frac{4x^{2}-3x+4}{x^{3}+4x}dx
y^{''}+2y^'+y=2e^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=2e^{-x}
derivative of 36x^2-72x	\frac{d}{dx}(36x^{2}-72x)
limit as x approaches 0 of cos(pi/x)	\lim\:_{x\to\:0}(\cos(\frac{π}{x}))
integral of (ln(x))/(x^{14)}	\int\:\frac{\ln(x)}{x^{14}}dx
integral of (1+sin(θ))^2	\int\:(1+\sin(θ))^{2}dθ
limit as x approaches-2+of x^2-5	\lim\:_{x\to\:-2+}(x^{2}-5)
y^{''}+y^'+2y=0,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y^{\prime\:}+2y=0,y(0)=0,y^{\prime\:}(0)=0
integral from 0 to pi of e^{-x}cos(2x)	\int\:_{0}^{π}e^{-x}\cos(2x)dx
(\partial)/(\partial y)(ln(x+e^{-y}))	\frac{\partial\:}{\partial\:y}(\ln(x+e^{-y}))
integral of cos(aln(x/b))	\int\:\cos(a\ln(\frac{x}{b}))dx
tangent of f(x)= 1/(x-2)	tangent\:f(x)=\frac{1}{x-2}
derivative of \sqrt[3]{1+tan(x})	\frac{d}{dx}(\sqrt[3]{1+\tan(x)})
y^'-2x(y^2+1)=0	y^{\prime\:}-2x(y^{2}+1)=0
derivative of (4x+1^2(1-x)^3)	\frac{d}{dx}((4x+1)^{2}(1-x)^{3})
limit as x approaches 0 of (x+1)/(x+4)	\lim\:_{x\to\:0}(\frac{x+1}{x+4})
((dy)/(dx))=((2x(y-1)))/(x^2+3)	(\frac{dy}{dx})=\frac{(2x(y-1))}{x^{2}+3}
sqrt(y^2+1)dx=xydy	\sqrt{y^{2}+1}dx=xydy
derivative of x/(x^2+t^2)	\frac{d}{dx}(\frac{x}{x^{2}+t^{2}})
integral from 0 to 3 of-x^2	\int\:_{0}^{3}-x^{2}dx
integral of tan(3x)sec^{5/4}(3x)	\int\:\tan(3x)\sec^{\frac{5}{4}}(3x)dx
tangent of y=sqrt(x),(36,6)	tangent\:y=\sqrt{x},(36,6)
derivative of log_{13}(x)	\frac{d}{dx}(\log_{13}(x))
derivative of f(x)=8x^2cot(x)	derivative\:f(x)=8x^{2}\cot(x)
d/(dt)(t/(1+t))	\frac{d}{dt}(\frac{t}{1+t})
sum from n=1 to infinity of 1/(ne^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{ne^{n}}
(d^6)/(dx^6)(x^{-6})	\frac{d^{6}}{dx^{6}}(x^{-6})
(\partial)/(\partial x)((x^2-a-1)(x^2+a-1))	\frac{\partial\:}{\partial\:x}((x^{2}-a-1)(x^{2}+a-1))
(\partial)/(\partial x)(3x^2+y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}+y^{2})
derivative of y=3x^2+e^2x+pi^2	derivative\:y=3x^{2}+e^{2}x+π^{2}
y=(1+4(2))^{3/2}	y=(1+4(2))^{\frac{3}{2}}
integral from 0 to x of sqrt(36-t^2)	\int\:_{0}^{x}\sqrt{36-t^{2}}dt
derivative of (2x^5-3^8)	\frac{d}{dx}((2x^{5}-3)^{8})
derivative of 4e^{x/2}	\frac{d}{dx}(4e^{\frac{x}{2}})
derivative of tan^2(3x)+1	derivative\:\tan^{2}(3x)+1
y^{''}+9y=3t^2	y^{\prime\:\prime\:}+9y=3t^{2}
derivative of pi*x^{1/2}-x^{1/3}	derivative\:π\cdot\:x^{\frac{1}{2}}-x^{\frac{1}{3}}
derivative of-4sin(x)	derivative\:-4\sin(x)
d/(db)(sin^4(2b)-cos^4(2b))	\frac{d}{db}(\sin^{4}(2b)-\cos^{4}(2b))
2x^2y-x^3y^'=y^3	2x^{2}y-x^{3}y^{\prime\:}=y^{3}
integral of (x^2)/(1+x^6)	\int\:\frac{x^{2}}{1+x^{6}}dx
integral of (x^2)/a e^{-x/a}	\int\:\frac{x^{2}}{a}e^{-\frac{x}{a}}dx

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