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Popular Calculus Problems

limit as x approaches infinity of 0(x)	\lim\:_{x\to\:\infty\:}(0(x))
integral of 15x^{3/2}	\int\:15x^{\frac{3}{2}}dx
(dy)/(dx)=(e^{2x+3y}),y(0)=0	\frac{dy}{dx}=(e^{2x+3y}),y(0)=0
derivative of (5-e^x^4)	\frac{d}{dx}((5-e^{x})^{4})
integral from 0 to 1/2 of (x^2)/(sqrt(1-x^2))	\int\:_{0}^{\frac{1}{2}}\frac{x^{2}}{\sqrt{1-x^{2}}}dx
(dy)/(dx)=3y-y^2	\frac{dy}{dx}=3y-y^{2}
integral of (ln(7x))/x	\int\:\frac{\ln(7x)}{x}dx
derivative of y=cos(sqrt(x))	derivative\:y=\cos(\sqrt{x})
d/(dt)(-3t)	\frac{d}{dt}(-3t)
derivative of f(x)=sqrt(x/5)	derivative\:f(x)=\sqrt{\frac{x}{5}}
derivative of (sqrt(1-sin^2(x))/(x^2))	\frac{d}{dx}(\frac{\sqrt{1-\sin^{2}(x)}}{x^{2}})
derivative of x^3-3x^2-9x+1	\frac{d}{dx}(x^{3}-3x^{2}-9x+1)
slope of (-3.2)(6.2)	slope\:(-3.2)(6.2)
integral of (8x^2+7x+8)/((x^2+1)^2)	\int\:\frac{8x^{2}+7x+8}{(x^{2}+1)^{2}}dx
limit as x approaches 5 of f(x)	\lim\:_{x\to\:5}(f(x))
derivative of f(x)=log_{4}(x^2-3x)	derivative\:f(x)=\log_{4}(x^{2}-3x)
(dy)/(dx)=e^{5y+6x},y(0)=2	\frac{dy}{dx}=e^{5y+6x},y(0)=2
derivative of ((1-5x)/((1+5x)))	\frac{d}{dx}(\frac{(1-5x)}{(1+5x)})
(dy)/(dx)=y(1-0.0002y)	\frac{dy}{dx}=y(1-0.0002y)
derivative of ln(x^2+4)	derivative\:\ln(x^{2}+4)
limit as x approaches 0 of 2f(x)-1	\lim\:_{x\to\:0}(2f(x)-1)
y^{''}+16y=4t^2	y^{\prime\:\prime\:}+16y=4t^{2}
integral of (x^4+9)/(x^2+9x^2)	\int\:\frac{x^{4}+9}{x^{2}+9x^{2}}dx
limit as x approaches 0 of (1+2x)^{-3/x}	\lim\:_{x\to\:0}((1+2x)^{-\frac{3}{x}})
(\partial)/(\partial x)(sin(pi(5x-5y)))	\frac{\partial\:}{\partial\:x}(\sin(π(5x-5y)))
derivative of f(x)=(x^3-8x^2+5)/(x^2)	derivative\:f(x)=\frac{x^{3}-8x^{2}+5}{x^{2}}
derivative of 3e^y	derivative\:3e^{y}
(\partial)/(\partial x)(xsin(2y))	\frac{\partial\:}{\partial\:x}(x\sin(2y))
derivative of-2x^2+5/3 x+11	\frac{d}{dx}(-2x^{2}+\frac{5}{3}x+11)
derivative of ln(sqrt((x^2-2/(x^2+2))))	\frac{d}{dx}(\ln(\sqrt{\frac{x^{2}-2}{x^{2}+2}}))
derivative of-5x^{4/5}+3x^{2/3}+2	\frac{d}{dx}(-5x^{\frac{4}{5}}+3x^{\frac{2}{3}}+2)
integral from-9 to 9 of sqrt(1+(x)^2)	\int\:_{-9}^{9}\sqrt{1+(x)^{2}}dx
limit as x approaches 9 of (\|x-9\|)/(x-9)	\lim\:_{x\to\:9}(\frac{\left\|x-9\right\|}{x-9})
(\partial)/(\partial x)((2y)/(3x))	\frac{\partial\:}{\partial\:x}(\frac{2y}{3x})
(x^2e^x+y)dx=xdy	(x^{2}e^{x}+y)dx=xdy
inverse oflaplace s/(s^2+3s+2)	inverselaplace\:\frac{s}{s^{2}+3s+2}
derivative of f(x)=(4x)/(5-cot(x))	derivative\:f(x)=\frac{4x}{5-\cot(x)}
integral of xe^{1/x}	\int\:xe^{\frac{1}{x}}dx
limit as x approaches-2 of (x^2-4)/(x+2)	\lim\:_{x\to\:-2}(\frac{x^{2}-4}{x+2})
derivative of e^{6/x}	derivative\:e^{\frac{6}{x}}
limit as x approaches 3.01 of x^2+3x	\lim\:_{x\to\:3.01}(x^{2}+3x)
x(dy)/(dx)=2xe^{x^2}-y+6x^2	x\frac{dy}{dx}=2xe^{x^{2}}-y+6x^{2}
y^'+y-3cos(x)=0	y^{\prime\:}+y-3\cos(x)=0
implicit (dy)/(dx),x^5+y^5=35xy	implicit\:\frac{dy}{dx},x^{5}+y^{5}=35xy
(\partial)/(\partial y)(e^{-1x}cos(6y))	\frac{\partial\:}{\partial\:y}(e^{-1x}\cos(6y))
derivative of (e^x)/(-8x^7)	derivative\:\frac{e^{x}}{-8x^{7}}
derivative of (x^5/(e^x))	\frac{d}{dx}(\frac{x^{5}}{e^{x}})
derivative of-(24/(x^5))	\frac{d}{dx}(-\frac{24}{x^{5}})
area y=x+20,y=x^2	area\:y=x+20,y=x^{2}
integral of (1+2x)^{-2}	\int\:(1+2x)^{-2}dx
y^{''}e^{ax}-2a^2ye^{ax}=0	y^{\prime\:\prime\:}e^{ax}-2a^{2}ye^{ax}=0
tangent of f(x)=sqrt(3x+7),\at x=6	tangent\:f(x)=\sqrt{3x+7},\at\:x=6
derivative of (1-3x)/(6+x)	derivative\:\frac{1-3x}{6+x}
derivative of f(x)= 1/((x+1)^2)	derivative\:f(x)=\frac{1}{(x+1)^{2}}
sum from n=1 to infinity of n/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{n}{2^{n}}
slope ofintercept (6,-1),(-3,-10)	slopeintercept\:(6,-1),(-3,-10)
d/(dy)((y^3)/(30)+5/(2y))	\frac{d}{dy}(\frac{y^{3}}{30}+\frac{5}{2y})
derivative of (x^2+1)^3	derivative\:(x^{2}+1)^{3}
tangent of y= 2/(x-8)	tangent\:y=\frac{2}{x-8}
limit as x approaches 1 of 1/(1-x^2)	\lim\:_{x\to\:1}(\frac{1}{1-x^{2}})
integral of 4x^2+4x+1	\int\:4x^{2}+4x+1dx
integral of 1/((y-3)^2)	\int\:\frac{1}{(y-3)^{2}}dy
(\partial)/(\partial z)(4e^xcos(yz))	\frac{\partial\:}{\partial\:z}(4e^{x}\cos(yz))
(\partial)/(\partial x)(x(x+y))	\frac{\partial\:}{\partial\:x}(x(x+y))
integral from-infinity to 2 of 1/(x^2+1)	\int\:_{-\infty\:}^{2}\frac{1}{x^{2}+1}dx
(\partial)/(\partial y)(e^x+yz)	\frac{\partial\:}{\partial\:y}(e^{x}+yz)
integral of 1/(e^z+e^{-z)}	\int\:\frac{1}{e^{z}+e^{-z}}dz
derivative of (3+x-2x^2^{1/4})	\frac{d}{dx}((3+x-2x^{2})^{\frac{1}{4}})
implicit (dy)/(dx),4x^2+9y^2=36	implicit\:\frac{dy}{dx},4x^{2}+9y^{2}=36
y^'+2xy=xe^{-x^2}	y^{\prime\:}+2xy=xe^{-x^{2}}
derivative of \sqrt[3]{2690-10x^2}	derivative\:\sqrt[3]{2690-10x^{2}}
integral of xsinh(mx)	\int\:x\sinh(mx)dx
integral of 2pix(x^2-1)^2	\int\:2πx(x^{2}-1)^{2}dx
integral from 4 to 9 of 4/(2sqrt(x))	\int\:_{4}^{9}\frac{4}{2\sqrt{x}}dx
derivative of f(x)=7arctan(7x),x=1	derivative\:f(x)=7\arctan(7x),x=1
sum from n=0 to infinity of n^2(1/3)^n	\sum\:_{n=0}^{\infty\:}n^{2}(\frac{1}{3})^{n}
integral of e^{-st}t^5	\int\:e^{-st}t^{5}dt
f^'(x)= 1/(3x^{2/3)}	f^{\prime\:}(x)=\frac{1}{3x^{\frac{2}{3}}}
integral of 3/56 x^2	\int\:\frac{3}{56}x^{2}dx
derivative of y=7(x^3+x^2) 2/3	derivative\:y=7(x^{3}+x^{2})\frac{2}{3}
derivative of 10(1.1^{x/2})	\frac{d}{dx}(10(1.1^{\frac{x}{2}}))
derivative of (x-1^2(2x+3))	\frac{d}{dx}((x-1)^{2}(2x+3))
integral from-3 to-1 of 1/(x^2+6x+13)	\int\:_{-3}^{-1}\frac{1}{x^{2}+6x+13}dx
integral of 1/((x+3)sqrt(x^2+6x+8))	\int\:\frac{1}{(x+3)\sqrt{x^{2}+6x+8}}dx
integral of (\sqrt[5]{x^4})	\int\:(\sqrt[5]{x^{4}})dx
7(ln(y))y^'-x^9y=0	7(\ln(y))y^{\prime\:}-x^{9}y=0
derivative of (f(4x))^2+5	derivative\:(f(4x))^{2}+5
derivative of log_{12}(x)	\frac{d}{dx}(\log_{12}(x))
derivative of (x^2/(2x^2+x+1))	\frac{d}{dx}(\frac{x^{2}}{2x^{2}+x+1})
(\partial)/(\partial x)(4y^3sin(2x))	\frac{\partial\:}{\partial\:x}(4y^{3}\sin(2x))
integral of 1/((3x-1)^3)	\int\:\frac{1}{(3x-1)^{3}}dx
derivative of 1/(sqrt(1+cos^2(2x)))	\frac{d}{dx}(\frac{1}{\sqrt{1+\cos^{2}(2x)}})
derivative of (ax^2+bx+ce^{(-x)/8})	\frac{d}{dx}((ax^{2}+bx+c)e^{\frac{-x}{8}})
integral of (x^2-2x+3)/(x^3+3x)	\int\:\frac{x^{2}-2x+3}{x^{3}+3x}dx
(\partial)/(\partial x)(1/(y^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{y^{2}})
xdx+ye^{-x}dy=0,y(0)=1	xdx+ye^{-x}dy=0,y(0)=1
(d^2y)/(dx^2)-4(dy)/(dx)+3y=0	\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+3y=0
y=cos(sin(sqrt(2x+5)))	y=\cos(\sin(\sqrt{2x+5}))
integral of sec^2(7x)	\int\:\sec^{2}(7x)dx
limit as x approaches+3 of (x-3)/(x^2-3)	\lim\:_{x\to\:+3}(\frac{x-3}{x^{2}-3})

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