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Popular Calculus Problems

implicit (dy)/(dx),ln(y)=x	implicit\:\frac{dy}{dx},\ln(y)=x
integral of y/1	\int\:\frac{y}{1}dy
d/(dt)(1-\|t\|)	\frac{d}{dt}(1-\left\|t\right\|)
integral of-sin(x)-e^{-x}+3x^2	\int\:-\sin(x)-e^{-x}+3x^{2}dx
y^{''}+5y^'+4y=8x^2+e^{-x}	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=8x^{2}+e^{-x}
(dy)/(dx)=2x(y-1)	\frac{dy}{dx}=2x(y-1)
integral of (sqrt(7-x^4))/(5x)	\int\:\frac{\sqrt{7-x^{4}}}{5x}dx
derivative of 7x-2y	derivative\:7x-2y
limit as x approaches-3 of (x^2+3)/4	\lim\:_{x\to\:-3}(\frac{x^{2}+3}{4})
limit as x approaches 1 of e	\lim\:_{x\to\:1}(e)
sum from n=1 to infinity of (1/3)^{k-n}	\sum\:_{n=1}^{\infty\:}(\frac{1}{3})^{k-n}
derivative of 5sec^2(x)	derivative\:5\sec^{2}(x)
f(x)=sec(x)tan(x)	f(x)=\sec(x)\tan(x)
area x^2-2x,2x-3	area\:x^{2}-2x,2x-3
integral from 0 to 1 of (93)/(x^5)	\int\:_{0}^{1}\frac{93}{x^{5}}dx
integral of (x^{1.3}+9x^{3.5})	\int\:(x^{1.3}+9x^{3.5})dx
integral of 5/((x-3)(x+2))	\int\:\frac{5}{(x-3)(x+2)}dx
derivative of (4x/(1-cot(x)))	\frac{d}{dx}(\frac{4x}{1-\cot(x)})
derivative of 2/(4-x)	derivative\:\frac{2}{4-x}
derivative of x-pi	\frac{d}{dx}(x-π)
tangent of y= 1/(x^4),(-2, 1/16)	tangent\:y=\frac{1}{x^{4}},(-2,\frac{1}{16})
integral of (2e^x)	\int\:(2e^{x})dx
limit as x approaches 0-of (x^2)/6-4/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{6}-\frac{4}{x})
integral of csc^2(3x-1)	\int\:\csc^{2}(3x-1)dx
integral from 0 to 1 of (24)/(x^2-9)	\int\:_{0}^{1}\frac{24}{x^{2}-9}dx
inverse oflaplace 1/(s^2+8)	inverselaplace\:\frac{1}{s^{2}+8}
integral of 3/(1+x)	\int\:\frac{3}{1+x}dx
derivative of e^{x^{3+6x^2}}	\frac{d}{dx}(e^{x^{3+6x^{2}}})
(dy)/(dt)= y/(1+t)-y/t+t^2(1+t)	\frac{dy}{dt}=\frac{y}{1+t}-\frac{y}{t}+t^{2}(1+t)
(\partial)/(\partial x)((13x-1)(3y-1))	\frac{\partial\:}{\partial\:x}((13x-1)(3y-1))
derivative of y=ln(3x-7)	derivative\:y=\ln(3x-7)
integral of (2x^3-x^2+2x+2)/(x^2+1)	\int\:\frac{2x^{3}-x^{2}+2x+2}{x^{2}+1}dx
taylor 1/(x-1),10	taylor\:\frac{1}{x-1},10
y^{''}+pi^2y=2	y^{\prime\:\prime\:}+π^{2}y=2
derivative of 2x^3-2x^2+12	derivative\:2x^{3}-2x^{2}+12
limit as x approaches 0 of-2-x	\lim\:_{x\to\:0}(-2-x)
(x^2+1)y^'+3x(y-1)=0,y(0)=3	(x^{2}+1)y^{\prime\:}+3x(y-1)=0,y(0)=3
derivative of x^2-6x+8	\frac{d}{dx}(x^{2}-6x+8)
derivative of (2x)/(1+x^2)	derivative\:\frac{2x}{1+x^{2}}
(d^2)/(dx^2)(\sqrt[6]{x})	\frac{d^{2}}{dx^{2}}(\sqrt[6]{x})
limit as x approaches 0-of 1	\lim\:_{x\to\:0-}(1)
sum from n=1 to infinity of ln(n+1)	\sum\:_{n=1}^{\infty\:}\ln(n+1)
derivative of f(x)=8x^2	derivative\:f(x)=8x^{2}
derivative of ln((x^2-81/k))	\frac{d}{dx}(\ln(\frac{x^{2}-81}{k}))
derivative of sqrt(6-7x)	derivative\:\sqrt{6-7x}
derivative of sin^{12}(3x^4-x)	\frac{d}{dx}(\sin^{12}(3x^{4}-x))
(dy)/(dx)=((2+y)^2)/(2x-1)	\frac{dy}{dx}=\frac{(2+y)^{2}}{2x-1}
laplacetransform 3t^2-9t	laplacetransform\:3t^{2}-9t
derivative of (4x+5)^{1/5}	derivative\:(4x+5)^{\frac{1}{5}}
derivative of arccos(x/5)	derivative\:\arccos(\frac{x}{5})
integral of (4x)/(x^2+5)	\int\:\frac{4x}{x^{2}+5}dx
(x^2+xy-y^2)dx+xydy=0	(x^{2}+xy-y^{2})dx+xydy=0
limit as x approaches 0 of (x-3)sqrt(x)	\lim\:_{x\to\:0}((x-3)\sqrt{x})
derivative of (3/4 ^x)	\frac{d}{dx}((\frac{3}{4})^{x})
(5x+3)+(5y-5)y^'=0	(5x+3)+(5y-5)y^{\prime\:}=0
integral of csc(x)	\int\:\csc(x)dx
derivative of sqrt((x^2+1^2))	\frac{d}{dx}(\sqrt{(x^{2}+1)^{2}})
integral of (x+1)^{10}	\int\:(x+1)^{10}dx
tangent of y=2x+3cos(x)	tangent\:y=2x+3\cos(x)
limit as x approaches 0 of f(x)	\lim\:_{x\to\:0}(f(x))
(\partial)/(\partial x)((4+5y)^x)	\frac{\partial\:}{\partial\:x}((4+5y)^{x})
limit as x approaches infinity of c^x	\lim\:_{x\to\:\infty\:}(c^{x})
limit as x approaches-infinity of 2	\lim\:_{x\to\:-\infty\:}(2)
y^'+ycos(x)=4cos(x),y(0)=6	y^{\prime\:}+y\cos(x)=4\cos(x),y(0)=6
slope of (-2.2)(1.2)	slope\:(-2.2)(1.2)
derivative of ln(sqrt((x+8/(x-8))))	\frac{d}{dx}(\ln(\sqrt{\frac{x+8}{x-8}}))
integral of (2x^2+4x-3)/(x^2)	\int\:\frac{2x^{2}+4x-3}{x^{2}}dx
y^{''}+121y=cos(10t)	y^{\prime\:\prime\:}+121y=\cos(10t)
integral of 2^{1/2}	\int\:2^{\frac{1}{2}}
(\partial)/(\partial x)(x^3y^3)	\frac{\partial\:}{\partial\:x}(x^{3}y^{3})
limit as x approaches+0 of (x^3)/(ln\|x\|)	\lim\:_{x\to\:+0}(\frac{x^{3}}{\ln\left\|x\right\|})
maclaurin sin(2x)+cos(2x)	maclaurin\:\sin(2x)+\cos(2x)
(\partial)/(\partial x)(e^{(y/x)})	\frac{\partial\:}{\partial\:x}(e^{(\frac{y}{x})})
derivative of sin(4/x)	derivative\:\sin(\frac{4}{x})
integral of x^2e^{-4x}	\int\:x^{2}e^{-4x}dx
area x=y^2+3,x=y,y=-1,y=1	area\:x=y^{2}+3,x=y,y=-1,y=1
sum from n=9 to infinity of 1/(n(n-1))	\sum\:_{n=9}^{\infty\:}\frac{1}{n(n-1)}
derivative of x^2-2x	derivative\:x^{2}-2x
integral of tan(x/4)	\int\:\tan(\frac{x}{4})dx
derivative of a/(1-bx)	derivative\:\frac{a}{1-bx}
(dy)/(dx)-5y=x^2	\frac{dy}{dx}-5y=x^{2}
taylor 7/x ,-1	taylor\:\frac{7}{x},-1
tangent of f(x)=sqrt(x^2+16),\at x=-3	tangent\:f(x)=\sqrt{x^{2}+16},\at\:x=-3
expand (x+5)cos(x)	expand\:(x+5)\cos(x)
y^{''}+4y^'+9y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+9y=0
integral of (x^2)/(sqrt(196-x^2))	\int\:\frac{x^{2}}{\sqrt{196-x^{2}}}dx
y^{''}+2y^'+37y=0,y(0)=-3,y^'(0)=21	y^{\prime\:\prime\:}+2y^{\prime\:}+37y=0,y(0)=-3,y^{\prime\:}(0)=21
d/(dy)((2-y^2+x^2)e^{(1-x^2-(y^2)/4)})	\frac{d}{dy}((2-y^{2}+x^{2})e^{(1-x^{2}-\frac{y^{2}}{4})})
derivative of 36e^{-2x}	\frac{d}{dx}(36e^{-2x})
derivative of f(x)=-3e^{4x}	derivative\:f(x)=-3e^{4x}
integral of-4x^{-5}	\int\:-4x^{-5}dx
integral of 1/((x^2))	\int\:\frac{1}{(x^{2})}dx
integral of (2x^2-x-1)(3x+4)	\int\:(2x^{2}-x-1)(3x+4)dx
derivative of sin^5(4x+1)	\frac{d}{dx}(\sin^{5}(4x+1))
y^'*(x^2+2)+4x(y^2+2y+1)=0	y^{\prime\:}\cdot\:(x^{2}+2)+4x(y^{2}+2y+1)=0
integral of (19)/(x^3-125)	\int\:\frac{19}{x^{3}-125}dx
(\partial)/(\partial x)(3)	\frac{\partial\:}{\partial\:x}(3)
derivative of f(x)=-12x^{3/2}+7x^{1.7}+x	derivative\:f(x)=-12x^{\frac{3}{2}}+7x^{1.7}+x
integral of (t^3)/(t^4+1)	\int\:\frac{t^{3}}{t^{4}+1}dt
integral of 2/(cos(x)-1)	\int\:\frac{2}{\cos(x)-1}dx

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