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Popular Calculus Problems

derivative of y=cos(a^7+x^7)	derivative\:y=\cos(a^{7}+x^{7})
d/(dt)(e^{-t}cos(t))	\frac{d}{dt}(e^{-t}\cos(t))
derivative of ln(x^3-63)	\frac{d}{dx}(\ln(x^{3}-63))
limit as x approaches 4 of 2	\lim\:_{x\to\:4}(2)
integral from-3 to 3 of x/(1+\|x\|)	\int\:_{-3}^{3}\frac{x}{1+\left\|x\right\|}dx
simplify-2/(x^3)+3/(x^2)-4x	simplify\:-\frac{2}{x^{3}}+\frac{3}{x^{2}}-4x
limit as x approaches 0 of ((cos(4x)-cos(6x)))/(cos(2x)sin^2(5x))	\lim\:_{x\to\:0}(\frac{(\cos(4x)-\cos(6x))}{\cos(2x)\sin^{2}(5x)})
y^'+y*sin(x)=sin(x)	y^{\prime\:}+y\cdot\:\sin(x)=\sin(x)
derivative of e^{-x}x-2e^{-x}	derivative\:e^{-x}x-2e^{-x}
(cos(x^2))^'	(\cos(x^{2}))^{\prime\:}
integral of cos(a)	\int\:\cos(a)
integral of sqrt(x^2+10)	\int\:\sqrt{x^{2}+10}dx
(sin(x))^'	(\sin(x))^{\prime\:}
integral from 0 to 2 of (x^2-1)	\int\:_{0}^{2}(x^{2}-1)dx
(cos(9x))y^'-9(tan(9x))y=9sec(9x)	(\cos(9x))y^{\prime\:}-9(\tan(9x))y=9\sec(9x)
integral of 1/(sqrt(3-4r-r^2))	\int\:\frac{1}{\sqrt{3-4r-r^{2}}}dr
integral of (3x^3+8x)/((x^2+2)^2)	\int\:\frac{3x^{3}+8x}{(x^{2}+2)^{2}}dx
(\partial)/(\partial x)(sqrt(p(q,x)q))	\frac{\partial\:}{\partial\:x}(\sqrt{p(q,x)q})
derivative of x(2x+3^4)	\frac{d}{dx}(x(2x+3)^{4})
integral of 1/x x'	\int\:\frac{1}{x}x\prime\:dx
derivative of sin(x/(1+y))	\frac{d}{dx}(\sin(\frac{x}{1+y}))
derivative of 5picos(pix)	\frac{d}{dx}(5π\cos(πx))
integral from-2 to 3 of (38)/(x^4)	\int\:_{-2}^{3}\frac{38}{x^{4}}dx
limit as x approaches-2 of-x^3+x	\lim\:_{x\to\:-2}(-x^{3}+x)
tangent of f(x)= x/((1+x^2)),\at x=3	tangent\:f(x)=\frac{x}{(1+x^{2})},\at\:x=3
integral from-3 to-1 of (x^2-4x+8)	\int\:_{-3}^{-1}(x^{2}-4x+8)dx
limit as x approaches-1 of 3^{2x}	\lim\:_{x\to\:-1}(3^{2x})
derivative of (x^2/(x^2-4))	\frac{d}{dx}(\frac{x^{2}}{x^{2}-4})
derivative of 2/(sqrt(x^2-3))	\frac{d}{dx}(\frac{2}{\sqrt{x^{2}-3}})
(dy}{dx}=\frac{(y^2-1))/x	\frac{dy}{dx}=\frac{(y^{2}-1)}{x}
derivative of y=34(3p+1)-2/5 ,p>0	derivative\:y=34(3p+1)-\frac{2}{5},p>0
(x+1)^'	(x+1)^{\prime\:}
integral of (2x-4+8sqrt(x))/(sqrt(x))	\int\:\frac{2x-4+8\sqrt{x}}{\sqrt{x}}dx
limit as x approaches 1 of (x^2-3x)/x	\lim\:_{x\to\:1}(\frac{x^{2}-3x}{x})
y^'+4/5 y=1-1/4 t	y^{\prime\:}+\frac{4}{5}y=1-\frac{1}{4}t
integral of 2/(sqrt(1-t^2))	\int\:\frac{2}{\sqrt{1-t^{2}}}dt
integral of (e^{3x})/x	\int\:\frac{e^{3x}}{x}dx
(\partial)/(\partial x)(-6e^y)	\frac{\partial\:}{\partial\:x}(-6e^{y})
integral of (1-x^3+5x^5-3x^7)	\int\:(1-x^{3}+5x^{5}-3x^{7})dx
derivative of 80picos(10pix)	\frac{d}{dx}(80π\cos(10πx))
(\partial)/(\partial x)(x^6+5xy^9)	\frac{\partial\:}{\partial\:x}(x^{6}+5xy^{9})
derivative of (8x^3-2x+9/x)	\frac{d}{dx}(\frac{8x^{3}-2x+9}{x})
derivative of 1/(4x^3+5x^2-7x+8)	\frac{d}{dx}(\frac{1}{4x^{3}+5x^{2}-7x+8})
integral of x(x^2+3)^7	\int\:x(x^{2}+3)^{7}dx
derivative of x^2en(x)	\frac{d}{dx}(x^{2}en(x))
derivative of y=tan(3x)	derivative\:y=\tan(3x)
integral of 1/((x-7)^2)-1	\int\:\frac{1}{(x-7)^{2}}-1dx
sum from n=1 to infinity of 1/(sqrt(2n))	\sum\:_{n=1}^{\infty\:}\frac{1}{\sqrt{2n}}
integral of ((x^2+2))/((x+2))	\int\:\frac{(x^{2}+2)}{(x+2)}dx
limit as x approaches 0 of 6x+\|x-5\|	\lim\:_{x\to\:0}(6x+\left\|x-5\right\|)
derivative of (2x^2+2x+8/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+2x+8}{\sqrt{x}})
derivative of f(x)=log_{2}(x)	derivative\:f(x)=\log_{2}(x)
limit as x approaches-3-of f(x)	\lim\:_{x\to\:-3-}(f(x))
integral of 2x+sin(x)+c	\int\:2x+\sin(x)+cdx
(\partial)/(\partial x)(x^4+x^2y)	\frac{\partial\:}{\partial\:x}(x^{4}+x^{2}y)
integral of (sqrt(441-x^2))/x	\int\:\frac{\sqrt{441-x^{2}}}{x}dx
tangent of y=-x^3+2x^2+1	tangent\:y=-x^{3}+2x^{2}+1
(\partial)/(\partial y)(ysin(x+y))	\frac{\partial\:}{\partial\:y}(y\sin(x+y))
derivative of e^{6x}ln(x^2-4)	\frac{d}{dx}(e^{6x}\ln(x^{2}-4))
integral from-1 to 2 of (x-6\|x\|)	\int\:_{-1}^{2}(x-6\left\|x\right\|)dx
integral of 1/(sqrt(-x^2+6x-5))	\int\:\frac{1}{\sqrt{-x^{2}+6x-5}}dx
4x^3y+x^4y^'=sin^3(x/9)	4x^{3}y+x^{4}y^{\prime\:}=\sin^{3}(\frac{x}{9})
taylor ln(x+1),0	taylor\:\ln(x+1),0
derivative of 3sin(2xcos(x))	\frac{d}{dx}(3\sin(2x)\cos(x))
(\partial)/(\partial t)(1)	\frac{\partial\:}{\partial\:t}(1)
derivative of f(x)=(x^2+2x+3)/(x^2+2x+1)	derivative\:f(x)=\frac{x^{2}+2x+3}{x^{2}+2x+1}
(\partial)/(\partial x)(-yz)	\frac{\partial\:}{\partial\:x}(-yz)
derivative of y=cos(sqrt(sin(tan(5x))))	derivative\:y=\cos(\sqrt{\sin(\tan(5x))})
derivative of 3^{sqrt(x^2+1)}	derivative\:3^{\sqrt{x^{2}+1}}
(\partial)/(\partial x)(x^ab^b)	\frac{\partial\:}{\partial\:x}(x^{a}b^{b})
integral of x/(4+9x^2)	\int\:\frac{x}{4+9x^{2}}dx
limit as t approaches 3 of (1/t-1/3)/(t-3)	\lim\:_{t\to\:3}(\frac{\frac{1}{t}-\frac{1}{3}}{t-3})
integral of 4000xe^{-0.2x}	\int\:4000xe^{-0.2x}dx
derivative of 4pix^2	\frac{d}{dx}(4πx^{2})
limit as x approaches-2 of 2	\lim\:_{x\to\:-2}(2)
integral of (sin^3(x))	\int\:(\sin^{3}(x))dx
tangent of f(x)=4x^3-4x,\at x=1	tangent\:f(x)=4x^{3}-4x,\at\:x=1
d/(dt)(t^2+5t)	\frac{d}{dt}(t^{2}+5t)
(\partial)/(\partial t)(ln(kx-mt))	\frac{\partial\:}{\partial\:t}(\ln(kx-mt))
f(x)=sqrt((x^2-1)/(x^2+1))	f(x)=\sqrt{\frac{x^{2}-1}{x^{2}+1}}
derivative of (4x/(9y))	\frac{d}{dx}(\frac{4x}{9y})
derivative of-7(3x^4+2^{-4})	\frac{d}{dx}(-7(3x^{4}+2)^{-4})
derivative of 2/(x^2+5)	\frac{d}{dx}(\frac{2}{x^{2}+5})
limit as x approaches 5 of (x+1)/(x-5)	\lim\:_{x\to\:5}(\frac{x+1}{x-5})
slope of (x^2-8)^4,\at x=3	slope\:(x^{2}-8)^{4},\at\:x=3
tangent of f(x)=7+4x^2-2x^3,\at x=1	tangent\:f(x)=7+4x^{2}-2x^{3},\at\:x=1
derivative of ce^x+ce^{-x}	\frac{d}{dx}(ce^{x}+ce^{-x})
derivative of (sqrt(x)/(x-1))	\frac{d}{dx}(\frac{\sqrt{x}}{x-1})
derivative of 1-cos(2x+2cos^2(x))	\frac{d}{dx}(1-\cos(2x)+2\cos^{2}(x))
integral of 6x^{13}e^{-x^7}	\int\:6x^{13}e^{-x^{7}}dx
limit as x approaches 0 of 4/(1+2^{1/x)}	\lim\:_{x\to\:0}(\frac{4}{1+2^{\frac{1}{x}}})
derivative of 4cos(4x)	\frac{d}{dx}(4\cos(4x))
f^'(x)=3x-4,f(-1)= 13/2	f^{\prime\:}(x)=3x-4,f(-1)=\frac{13}{2}
integral of 1/(5-7x)	\int\:\frac{1}{5-7x}dx
y^{''''}+4y^{''}+4y=0	y^{\prime\:\prime\:\prime\:\prime\:}+4y^{\prime\:\prime\:}+4y=0
(\partial)/(\partial x)(2xy^2-2x^3y)	\frac{\partial\:}{\partial\:x}(2xy^{2}-2x^{3}y)
sum from n=0 to infinity of (((1)^n))/n	\sum\:_{n=0}^{\infty\:}\frac{((1)^{n})}{n}
derivative of y=(x^2+1)/(2x^2-1)	derivative\:y=\frac{x^{2}+1}{2x^{2}-1}
derivative of 1-cos(x-1)	\frac{d}{dx}(1-\cos(x-1))
tangent of f(x)=12sqrt(x)-2x,\at x=9	tangent\:f(x)=12\sqrt{x}-2x,\at\:x=9

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