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Popular Calculus Problems

(d^2y)/(dx^2)+2/x (dy)/(dx)=3xx	\frac{d^{2}y}{dx^{2}}+\frac{2}{x}\frac{dy}{dx}=3xx
tangent of f(x)=(x^2+7)(5x+4),\at x=2	tangent\:f(x)=(x^{2}+7)(5x+4),\at\:x=2
limit as x approaches 0 of 9	\lim\:_{x\to\:0}(9)
integral of 1/(cos^2(3x))	\int\:\frac{1}{\cos^{2}(3x)}dx
integral of e	\int\:e
y^'=(2x^7e^{y/x}+x^5y^2)/(x^6y)	y^{\prime\:}=\frac{2x^{7}e^{\frac{y}{x}}+x^{5}y^{2}}{x^{6}y}
(dy)/(dt)=1y,y(1)=3	\frac{dy}{dt}=1y,y(1)=3
derivative of 3x^3+5x^2-4x+10	\frac{d}{dx}(3x^{3}+5x^{2}-4x+10)
integral of tan^2(6x)sec^4(6x)	\int\:\tan^{2}(6x)\sec^{4}(6x)dx
area x^3,-x,8	area\:x^{3},-x,8
derivative of sqrt((2x-y))	\frac{d}{dx}(\sqrt{(2x-y)})
d/(dt)(t^4)	\frac{d}{dt}(t^{4})
integral from 0 to 6 of 9sqrt(4x+1)	\int\:_{0}^{6}9\sqrt{4x+1}dx
36y^{''}-y=0,y(-5)=1,y^'(-5)=-1	36y^{\prime\:\prime\:}-y=0,y(-5)=1,y^{\prime\:}(-5)=-1
y^{''}-y^'=0	y^{\prime\:\prime\:}-y^{\prime\:}=0
limit as x approaches 2+of tan((pix)/4)	\lim\:_{x\to\:2+}(\tan(\frac{πx}{4}))
integral from 1 to infinity of 2^{-x}	\int\:_{1}^{\infty\:}2^{-x}dx
tangent of f(x)=(x^3+2)^5,\at x=-1	tangent\:f(x)=(x^{3}+2)^{5},\at\:x=-1
taylor sqrt(x),1	taylor\:\sqrt{x},1
derivative of sqrt(4-3x^2)	\frac{d}{dx}(\sqrt{4-3x^{2}})
area y=x^3-6x^2+8x,y=x^2-4x	area\:y=x^{3}-6x^{2}+8x,y=x^{2}-4x
derivative of ln(xe^{sqrt(x)}+2)	derivative\:\ln(xe^{\sqrt{x}}+2)
derivative of (2cot(x)/(csc(x)))	\frac{d}{dx}(\frac{2\cot(x)}{\csc(x)})
derivative of In(-x^2+6x)	\frac{d}{dx}(In(-x^{2}+6x))
limit as x approaches 1+of (x+9)/(x+2)	\lim\:_{x\to\:1+}(\frac{x+9}{x+2})
(\partial)/(\partial x)(4yx^3-12y^2x^2)	\frac{\partial\:}{\partial\:x}(4yx^{3}-12y^{2}x^{2})
inverse oflaplace se^{-s}	inverselaplace\:se^{-s}
limit as x approaches 0+of x^{3/x}	\lim\:_{x\to\:0+}(x^{\frac{3}{x}})
derivative of cos(6x^3-4)	\frac{d}{dx}(\cos(6x^{3}-4))
laplacetransform e^{-2((t-1))}*1((t-1))	laplacetransform\:e^{-2((t-1))}\cdot\:1((t-1))
integral from 0 to 7 of e^xsin(x)	\int\:_{0}^{7}e^{x}\sin(x)dx
derivative of 2x^3-48x^2	\frac{d}{dx}(2x^{3}-48x^{2})
integral of sqrt(2x-1)	\int\:\sqrt{2x-1}dx
integral of 16θsec^2(θ)	\int\:16θ\sec^{2}(θ)dθ
y^{''}-6y^'+9y=0,y(0)=4,y^'(0)=0	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=4,y^{\prime\:}(0)=0
integral from-1/3 to 0 of 3/4 (1-x^2)	\int\:_{-\frac{1}{3}}^{0}\frac{3}{4}(1-x^{2})dx
derivative of sqrt(x)+x^2+ln(x)	derivative\:\sqrt{x}+x^{2}+\ln(x)
limit as x approaches+2pi of f(x)	\lim\:_{x\to\:+2π}(f(x))
derivative of ln(x^3+3x)	derivative\:\ln(x^{3}+3x)
(dx)/(dy)=5x+y	\frac{dx}{dy}=5x+y
(dy)/(dx)=y^2,y(1)=1	\frac{dy}{dx}=y^{2},y(1)=1
integral of (2x+1)/(x(x+1)^2)	\int\:\frac{2x+1}{x(x+1)^{2}}dx
integral of (x-2)	\int\:(x-2)dx
integral from 0 to 1 of xcos(2x^2+7)	\int\:_{0}^{1}x\cos(2x^{2}+7)dx
(\partial)/(\partial x)(sqrt(xy^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{xy^{2}+y^{2}})
integral from 1 to 3 of 2r^4ln(r)	\int\:_{1}^{3}2r^{4}\ln(r)dr
slope of (-4,-4),(2,5)	slope\:(-4,-4),(2,5)
integral of (4x-3)(2x-1)	\int\:(4x-3)(2x-1)dx
(\partial)/(\partial x)(x^3y+xy^2-2x^2-y^2)	\frac{\partial\:}{\partial\:x}(x^{3}y+xy^{2}-2x^{2}-y^{2})
integral of (x-1)/(x+2)	\int\:\frac{x-1}{x+2}dx
integral of u*sec^2(u)	\int\:u\cdot\:\sec^{2}(u)du
derivative of f(x)=8x^3	derivative\:f(x)=8x^{3}
derivative of (sec^2(x)dx)	\frac{d}{dx}((\sec^{2}(x))dx)
derivative of f(t)=t^6sin(t)	derivative\:f(t)=t^{6}\sin(t)
derivative of cos(-x)	derivative\:\cos(-x)
(\partial)/(\partial y)(5x+4y)	\frac{\partial\:}{\partial\:y}(5x+4y)
integral of 2xe^{3x^2}	\int\:2xe^{3x^{2}}dx
limit as x approaches+(-1) of x-1	\lim\:_{x\to\:+(-1)}(x-1)
integral from 0 to 2 of pi(4/(x^2+4))^2	\int\:_{0}^{2}π(\frac{4}{x^{2}+4})^{2}dx
limit as x approaches 0 of ((sin(x)))/x	\lim\:_{x\to\:0}(\frac{(\sin(x))}{x})
(\partial)/(\partial x)(-x^3+6x^2y^3+5y^2)	\frac{\partial\:}{\partial\:x}(-x^{3}+6x^{2}y^{3}+5y^{2})
integral of (2x+3)/((2x^2+6x)^4)	\int\:\frac{2x+3}{(2x^{2}+6x)^{4}}dx
(dx)/(dt)= 1/(t(1-t))	\frac{dx}{dt}=\frac{1}{t(1-t)}
d/(dt)(xy)	\frac{d}{dt}(xy)
derivative of 7xsin(pix)	derivative\:7x\sin(πx)
integral of (x-1/(x^2))	\int\:(x-\frac{1}{x^{2}})dx
integral of ln(5^x)	\int\:\ln(5^{x})dx
derivative of 9t^2+sqrt(t^3)	derivative\:9t^{2}+\sqrt{t^{3}}
integral of e^{-sx}x	\int\:e^{-sx}xdx
laplacetransform t^2cos(2t)	laplacetransform\:t^{2}\cos(2t)
derivative of log_{10}(2x-3)	\frac{d}{dx}(\log_{10}(2x-3))
integral of (x^2+12x-4)/(x^3-4x)	\int\:\frac{x^{2}+12x-4}{x^{3}-4x}dx
(\partial)/(\partial x)(4xln(y)+yln(z)-4x)	\frac{\partial\:}{\partial\:x}(4x\ln(y)+y\ln(z)-4x)
integral of (x^2)/(x-10)	\int\:\frac{x^{2}}{x-10}dx
(dy)/(dx)=(4x+y)^2	\frac{dy}{dx}=(4x+y)^{2}
derivative of (x^3-1/(x-1))	\frac{d}{dx}(\frac{x^{3}-1}{x-1})
(\partial)/(\partial x)(ln(10x))	\frac{\partial\:}{\partial\:x}(\ln(10x))
derivative of x/(log_{e(x)})	\frac{d}{dx}(\frac{x}{\log_{e}(x)})
derivative of be^{-x}	\frac{d}{dx}(be^{-x})
integral of (x^{3/2}+2x+1)	\int\:(x^{\frac{3}{2}}+2x+1)dx
limit as h approaches 0 of (2/(1+h)-2)/h	\lim\:_{h\to\:0}(\frac{\frac{2}{1+h}-2}{h})
derivative of-7x^4+7x^3-x^2+x	derivative\:-7x^{4}+7x^{3}-x^{2}+x
integral of (sec(3x))/(cot(3x))	\int\:\frac{\sec(3x)}{\cot(3x)}dx
(\partial)/(\partial y)(y/(2x+3y))	\frac{\partial\:}{\partial\:y}(\frac{y}{2x+3y})
integral from 0 to 2pi of (cos(x))^2	\int\:_{0}^{2π}(\cos(x))^{2}dx
derivative of (2x^2+6x+2)/(sqrt(x))	derivative\:\frac{2x^{2}+6x+2}{\sqrt{x}}
integral of sec^2(x)sqrt(tan(x))	\int\:\sec^{2}(x)\sqrt{\tan(x)}dx
(1/x+2y^2x)dx+(2yx^2-cos(y))dy=0,y(1)=pi	(\frac{1}{x}+2y^{2}x)dx+(2yx^{2}-\cos(y))dy=0,y(1)=π
sum from n=1 to infinity of (sin(3))^n	\sum\:_{n=1}^{\infty\:}(\sin(3))^{n}
derivative of e^{x+y}-1	\frac{d}{dx}(e^{x+y}-1)
integral of (sin^4(x))/(cos^6(x))	\int\:\frac{\sin^{4}(x)}{\cos^{6}(x)}dx
tangent of f(x)=7sqrt(x),\at x=4	tangent\:f(x)=7\sqrt{x},\at\:x=4
sum from n=5 to infinity of (n^3)/(2^n)	\sum\:_{n=5}^{\infty\:}\frac{n^{3}}{2^{n}}
f^{''}(x)=2	f^{\prime\:\prime\:}(x)=2
limit as x approaches-infinity of x+1/x	\lim\:_{x\to\:-\infty\:}(x+\frac{1}{x})
integral from 0 to pi/4 of sec(x)	\int\:_{0}^{\frac{π}{4}}\sec(x)dx
integral of 24x^5	\int\:24x^{5}dx
integral of 2sqrt(x)ln(x)	\int\:2\sqrt{x}\ln(x)dx
derivative of cos(4e^{-8x})	\frac{d}{dx}(\cos(4e^{-8x}))
tangent of f(x)=x+2/x ,(2,3)	tangent\:f(x)=x+\frac{2}{x},(2,3)

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