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Popular Calculus Problems

tangent of x+5/x	tangent\:x+\frac{5}{x}
(xdy)/(dx)-y=x^{2017}*y^2	\frac{xdy}{dx}-y=x^{2017}\cdot\:y^{2}
(\partial)/(\partial x)((2-xy)e^{-xy})	\frac{\partial\:}{\partial\:x}((2-xy)e^{-xy})
(\partial)/(\partial x)((2x+2y)e^y)	\frac{\partial\:}{\partial\:x}((2x+2y)e^{y})
integral of (2y)/(x^2+1)	\int\:\frac{2y}{x^{2}+1}dy
integral of x+y+z	\int\:x+y+zdx
derivative of-2x^2+3x-4	\frac{d}{dx}(-2x^{2}+3x-4)
(dy}{dx}=\frac{3y)/x ,x>0	\frac{dy}{dx}=\frac{3y}{x},x>0
integral of 3/(xln(x))	\int\:\frac{3}{x\ln(x)}dx
derivative of (x^3/(39)+(13)/(4x))	\frac{d}{dx}(\frac{x^{3}}{39}+\frac{13}{4x})
derivative of f(x)= 2/(t^3)	derivative\:f(x)=\frac{2}{t^{3}}
implicit (d^2y)/(dx^2),x^2+y^2=16	implicit\:\frac{d^{2}y}{dx^{2}},x^{2}+y^{2}=16
(\partial)/(\partial z)(xy+yz-xz)	\frac{\partial\:}{\partial\:z}(xy+yz-xz)
sqrt(1-y^2)dx=sqrt(1-x^2)dy	\sqrt{1-y^{2}}dx=\sqrt{1-x^{2}}dy
limit as x approaches 0 of (-2e^{-x})/(2x-2)	\lim\:_{x\to\:0}(\frac{-2e^{-x}}{2x-2})
integral of (e^{4x})/(-4x)	\int\:\frac{e^{4x}}{-4x}dx
limit as x approaches+0 of ((3e^x-3))/x	\lim\:_{x\to\:+0}(\frac{(3e^{x}-3)}{x})
integral from 0 to 1 of 0.5e^{-2x}	\int\:_{0}^{1}0.5e^{-2x}dx
integral of 2xx	\int\:2xxdx
derivative of (x+1)/(3x^2+6x+7)	derivative\:\frac{x+1}{3x^{2}+6x+7}
integral of sin^2(wt)	\int\:\sin^{2}(wt)dt
maclaurin arctan(4x)	maclaurin\:\arctan(4x)
derivative of (x^{-2}+x^3*(4x)^{-2x})	\frac{d}{dx}((x^{-2}+x)^{3}\cdot\:(4x)^{-2x})
(\partial)/(\partial x)(l-c)	\frac{\partial\:}{\partial\:x}(l-c)
integral of x(15x+4)	\int\:x(15x+4)dx
derivative of ((6x^2+6x+4))/(sqrt(x))	derivative\:\frac{(6x^{2}+6x+4)}{\sqrt{x}}
derivative of xy^4	\frac{d}{dx}(xy^{4})
derivative of (x^2-9^3)	\frac{d}{dx}((x^{2}-9)^{3})
integral of x^{37}sin(x^{38})	\int\:x^{37}\sin(x^{38})dx
integral of sec(x/8)	\int\:\sec(\frac{x}{8})dx
integral from 8 to infinity of xe^{-5x}	\int\:_{8}^{\infty\:}xe^{-5x}dx
derivative of 12e^{x/2}	\frac{d}{dx}(12e^{\frac{x}{2}})
integral of (e^x(xln(x)+1))/x	\int\:\frac{e^{x}(x\ln(x)+1)}{x}dx
derivative of (3x+8)/(x^2)	derivative\:\frac{3x+8}{x^{2}}
inverse oflaplace ((3s+1))/(s+2)	inverselaplace\:\frac{(3s+1)}{s+2}
(\partial)/(\partial y)(x/((x+y)^2))	\frac{\partial\:}{\partial\:y}(\frac{x}{(x+y)^{2}})
integral from 1 to 3 of (x^3+1/(4x^3))	\int\:_{1}^{3}(x^{3}+\frac{1}{4x^{3}})dx
normal of y=2x-1+4x^2,(1,5)	normal\:y=2x-1+4x^{2},(1,5)
integral of ke^{-x}	\int\:ke^{-x}dx
(\partial)/(\partial x)(y(e^x+xe^x))	\frac{\partial\:}{\partial\:x}(y(e^{x}+xe^{x}))
derivative of g(x)= 1/(4x^2+2x)	derivative\:g(x)=\frac{1}{4x^{2}+2x}
laplacetransform 2t+3t*cos(2t)	laplacetransform\:2t+3t\cdot\:\cos(2t)
derivative of cxe^{-x}	\frac{d}{dx}(cxe^{-x})
integral of 2x*sin(x)e^x	\int\:2x\cdot\:\sin(x)e^{x}dx
t*ty^{''}+5ty^'+4y=0	t\cdot\:ty^{\prime\:\prime\:}+5ty^{\prime\:}+4y=0
((sqrt(x^2+25))/2+(9-x)/3)^'	(\frac{\sqrt{x^{2}+25}}{2}+\frac{9-x}{3})^{\prime\:}
integral of x^7-4x^{-3}+1	\int\:x^{7}-4x^{-3}+1dx
integral of 4xe^{-x^2}	\int\:4xe^{-x^{2}}dx
y^'+y=-1	y^{\prime\:}+y=-1
derivative of tan(arccos(x))	\frac{d}{dx}(\tan(\arccos(x)))
integral from 0 to 1 of (x+1)^3	\int\:_{0}^{1}(x+1)^{3}dx
limit as x approaches-1 of 2-3x	\lim\:_{x\to\:-1}(2-3x)
limit as x approaches infinity of 8-2x	\lim\:_{x\to\:\infty\:}(8-2x)
(\partial)/(\partial y)(x^2+y^2-1)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-1)
derivative of-(14/(x^6))	\frac{d}{dx}(-\frac{14}{x^{6}})
expand 4(2t-5)^2	expand\:4(2t-5)^{2}
integral of x^2*sqrt(x^2-9)	\int\:x^{2}\cdot\:\sqrt{x^{2}-9}dx
(dP)/(dt)=0.5(P)(1-P/(1000))	\frac{dP}{dt}=0.5(P)(1-\frac{P}{1000})
(dy)/(dx)=(3sec(y))/((x+1)^2)	\frac{dy}{dx}=\frac{3\sec(y)}{(x+1)^{2}}
derivative of f(x)=(4x)/((x^2+1)^2)	derivative\:f(x)=\frac{4x}{(x^{2}+1)^{2}}
sum from n=1 to infinity of n(sin(npi))	\sum\:_{n=1}^{\infty\:}n(\sin(nπ))
derivative of (1-x^2(1+x)^3)	\frac{d}{dx}((1-x)^{2}(1+x)^{3})
sum from n=1 to infinity of (3n)/(-2n+5)	\sum\:_{n=1}^{\infty\:}\frac{3n}{-2n+5}
derivative of 2e^{3t}	derivative\:2e^{3t}
derivative of 3600(1-t/(60))^2	derivative\:3600(1-\frac{t}{60})^{2}
limit as x approaches 3 of (\|x+3\|)/(x+3)	\lim\:_{x\to\:3}(\frac{\left\|x+3\right\|}{x+3})
derivative of 4/(x^4+1/x+2)	\frac{d}{dx}(\frac{4}{x^{4}}+\frac{1}{x}+2)
limit as x approaches 0 of (1+sin(3x))^{1/x}	\lim\:_{x\to\:0}((1+\sin(3x))^{\frac{1}{x}})
derivative of (pix^2/2)	\frac{d}{dx}(\frac{πx^{2}}{2})
derivative of (1+sin(x)cos(x))	\frac{d}{dx}((1+\sin(x))\cos(x))
integral of (7x^6+6)/(x^7+6x)	\int\:\frac{7x^{6}+6}{x^{7}+6x}dx
integral of sqrt(e^{10x)-9}	\int\:\sqrt{e^{10x}-9}dx
sum from n=3 to infinity of 2/(5^n)	\sum\:_{n=3}^{\infty\:}\frac{2}{5^{n}}
limit as x approaches 0+of x+\|x\|	\lim\:_{x\to\:0+}(x+\left\|x\right\|)
derivative of (3x^2+4^2(4x^2-8)^2)	\frac{d}{dx}((3x^{2}+4)^{2}(4x^{2}-8)^{2})
y^{''}+8y^'+16y=0,y(1)=0,y^'(1)=1	y^{\prime\:\prime\:}+8y^{\prime\:}+16y=0,y(1)=0,y^{\prime\:}(1)=1
derivative of (x^4+3x^2-2)^5	derivative\:(x^{4}+3x^{2}-2)^{5}
(x+1)y^'+(x+2)y=8xe^{-x}	(x+1)y^{\prime\:}+(x+2)y=8xe^{-x}
integral of 8x^3e^{x^4}	\int\:8x^{3}e^{x^{4}}dx
derivative of 8sqrt(x)sin(x)	derivative\:8\sqrt{x}\sin(x)
area 1-x^2,13-7x	area\:1-x^{2},13-7x
(\partial)/(\partial x)(e^{8x}cos(5y))	\frac{\partial\:}{\partial\:x}(e^{8x}\cos(5y))
derivative of 5csc(x)	\frac{d}{dx}(5\csc(x))
limit as x approaches a of x^2	\lim\:_{x\to\:a}(x^{2})
integral of 1/(t^2)sin(8/t+3)	\int\:\frac{1}{t^{2}}\sin(\frac{8}{t}+3)dt
inverse oflaplace 3+1/s	inverselaplace\:3+\frac{1}{s}
integral from o to 1 of 42x(1-x)^5	\int\:_{o}^{1}42x(1-x)^{5}dx
derivative of a^2+x^2	\frac{d}{dx}(a^{2}+x^{2})
limit as x approaches 1 of (1+x)/(1-x^2)	\lim\:_{x\to\:1}(\frac{1+x}{1-x^{2}})
integral from 0 to-pi/6 of xcos(3x)	\int\:_{0}^{-\frac{π}{6}}x\cos(3x)dx
derivative of y=8x+7	derivative\:y=8x+7
limit as t approaches 1 of sqrt(t+8)	\lim\:_{t\to\:1}(\sqrt{t+8})
(\partial)/(\partial x)(4e^x-2x*e^y)	\frac{\partial\:}{\partial\:x}(4\cdot\:e^{x}-2\cdot\:x\cdot\:e^{y})
derivative of (4x-1^{1/3})	\frac{d}{dx}((4x-1)^{\frac{1}{3}})
derivative of (x^4+6x-1)/(7x^2-6x+1)	derivative\:\frac{x^{4}+6x-1}{7x^{2}-6x+1}
derivative of sin(15x)	derivative\:\sin(15x)
integral of sqrt(6-x^2)	\int\:\sqrt{6-x^{2}}dx
y^'=(sqrt(1-y^2))/t	y^{\prime\:}=\frac{\sqrt{1-y^{2}}}{t}
tangent of f(x)=4x^2+2x,(-2,12)	tangent\:f(x)=4x^{2}+2x,(-2,12)
integral of (x^7)/2-1/(x^5)	\int\:\frac{x^{7}}{2}-\frac{1}{x^{5}}dx

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