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Popular Calculus Problems

derivative of arccos(sqrt(y-2x))	\frac{d}{dx}(\arccos(\sqrt{y-2x}))
integral of sec^2(θ)tan^7(θ)	\int\:\sec^{2}(θ)\tan^{7}(θ)dθ
limit as x approaches 2 of (-1)/((x+2))	\lim\:_{x\to\:2}(\frac{-1}{(x+2)})
derivative of (2-x/(1+2x^2))	\frac{d}{dx}(\frac{2-x}{1+2x^{2}})
limit as x approaches 0 of sqrt(16-7x)	\lim\:_{x\to\:0}(\sqrt{16-7x})
integral of-cos(x)+C	\int\:-\cos(x)+Cdx
d/(dt)(4e^{-t})	\frac{d}{dt}(4e^{-t})
derivative of 4x^2-2	derivative\:4x^{2}-2
derivative of 3sqrt(4-1/2 x)	\frac{d}{dx}(3\sqrt{4-\frac{1}{2}x})
integral of x*sin(4x)	\int\:x\cdot\:\sin(4x)dx
derivative of (-2x/(x^2+1))	\frac{d}{dx}(\frac{-2x}{x^{2}+1})
integral of 12e^{3x-1}	\int\:12e^{3x-1}dx
integral of 6/((1-2x)^3)	\int\:\frac{6}{(1-2x)^{3}}dx
x(dy)/(dx)+y=-6xy^2	x\frac{dy}{dx}+y=-6xy^{2}
limit as x approaches 2 of sqrt(2x^2-4x)	\lim\:_{x\to\:2}(\sqrt{2x^{2}-4x})
integral of (3x^2)/(sqrt(1-6x^3))	\int\:\frac{3x^{2}}{\sqrt{1-6x^{3}}}dx
(\partial)/(\partial x)(ysin(z))	\frac{\partial\:}{\partial\:x}(y\sin(z))
limit as x approaches-8-of (x+2)/(x+8)	\lim\:_{x\to\:-8-}(\frac{x+2}{x+8})
area 8x-10,x^2-4x+10	area\:8x-10,x^{2}-4x+10
implicit (dy)/(dx),e^xy=1	implicit\:\frac{dy}{dx},e^{x}y=1
integral of x^2-2	\int\:x^{2}-2dx
d/(d{x)}(({y})/(sqrt({x)^2+{y)^2+{z}^2}})	\frac{d}{d{x}}(\frac{{y}}{\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}})
(dy)/(dx)=(2y)/(3x)	\frac{dy}{dx}=\frac{2y}{3x}
tangent of f(x)=sqrt(5-3x),\at x=-2	tangent\:f(x)=\sqrt{5-3x},\at\:x=-2
limit as x approaches-5 of 4x^3+x	\lim\:_{x\to\:-5}(4x^{3}+x)
(dy)/(dx)+3y=2	\frac{dy}{dx}+3y=2
limit as x approaches 3 of-8	\lim\:_{x\to\:3}(-8)
integral of 1/((3+x)^2)	\int\:\frac{1}{(3+x)^{2}}dx
d/(dt)(ln(sqrt((a+bt)/(a-bt))))	\frac{d}{dt}(\ln(\sqrt{\frac{a+bt}{a-bt}}))
d/(ds)(2/(s^2+4))	\frac{d}{ds}(\frac{2}{s^{2}+4})
integral from 1 to 2 of x^2	\int\:_{1}^{2}x^{2}dx
integral from 0 to 2 of x/(sqrt(16-x^2))	\int\:_{0}^{2}\frac{x}{\sqrt{16-x^{2}}}dx
integral of 5/(2x+7)	\int\:\frac{5}{2x+7}dx
limit as x approaches 2 of (x+4)/(3x-1)	\lim\:_{x\to\:2}(\frac{x+4}{3x-1})
integral of 1/((4x^2-1)^2)	\int\:\frac{1}{(4x^{2}-1)^{2}}dx
integral of 2x(x^2+8)^7	\int\:2x(x^{2}+8)^{7}dx
(\partial)/(\partial x)((y-x^2)^2+x^5)	\frac{\partial\:}{\partial\:x}((y-x^{2})^{2}+x^{5})
taylor g(x)= 1/((1+2x)^3)	taylor\:g(x)=\frac{1}{(1+2x)^{3}}
taylor 1-cos(x)	taylor\:1-\cos(x)
integral from-pi to pi of pisin^2(x)	\int\:_{-π}^{π}π\sin^{2}(x)dx
sum from n=1 to infinity}(((-2)^{n-1 of))/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{((-2)^{n-1})}{7^{n}}
integral from 0 to 1 of (-4y)/(e^{2y)}	\int\:_{0}^{1}\frac{-4y}{e^{2y}}dy
(\partial)/(\partial x)(6x^2y+9xy^3)	\frac{\partial\:}{\partial\:x}(6x^{2}y+9xy^{3})
(\partial)/(\partial x)(-xy(12-x-y))	\frac{\partial\:}{\partial\:x}(-xy(12-x-y))
(\partial)/(\partial t)(ln(x+t^2))	\frac{\partial\:}{\partial\:t}(\ln(x+t^{2}))
derivative of (7+8x-4sqrt(x)/x)	\frac{d}{dx}(\frac{7+8x-4\sqrt{x}}{x})
integral from 3 to 6 of 2pix(-3/2 x+9)	\int\:_{3}^{6}2πx(-\frac{3}{2}x+9)dx
integral of (sqrt(484-x^2))/x	\int\:\frac{\sqrt{484-x^{2}}}{x}dx
integral of u/(2u+1)	\int\:\frac{u}{2u+1}du
area x^3,x+6=y,(-x)/2 =y	area\:x^{3},x+6=y,\frac{-x}{2}=y
(\partial)/(\partial y)(ln(sqrt(xy)))	\frac{\partial\:}{\partial\:y}(\ln(\sqrt{xy}))
integral of (1/(xsqrt(x^2-1)))	\int\:(\frac{1}{x\sqrt{x^{2}-1}})dx
(d^2)/(dx^2)((-5x+6)^5)	\frac{d^{2}}{dx^{2}}((-5x+6)^{5})
y^{''}+4y^'+5y=-5x+3e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=-5x+3e^{-x}
integral of-csc(2w)cot(2w)	\int\:-\csc(2w)\cot(2w)dw
d/(dθ)(cos(θ)-2sin(θ))	\frac{d}{dθ}(\cos(θ)-2\sin(θ))
limit as x approaches 0-of ax^2+b/2	\lim\:_{x\to\:0-}(ax^{2}+\frac{b}{2})
tangent of 2/(x^2),\at (1.2)	tangent\:\frac{2}{x^{2}},\at\:(1.2)
integral of 1/(xln^4(x))	\int\:\frac{1}{x\ln^{4}(x)}dx
y^'=y^{1/3}	y^{\prime\:}=y^{\frac{1}{3}}
(dy)/(dx)=5x+15y	\frac{dy}{dx}=5x+15y
f(x)= x/(4x+3ln(x))	f(x)=\frac{x}{4x+3\ln(x)}
slope of y=(-4x^2+12)/(2x+2)	slope\:y=\frac{-4x^{2}+12}{2x+2}
derivative of (2x-3x^3tan(x))	\frac{d}{dx}((2x-3x^{3})\tan(x))
derivative of arcsin(e^{-x})	\frac{d}{dx}(\arcsin(e^{-x}))
area y=ln(x),x=e,y=0	area\:y=\ln(x),x=e,y=0
limit as x approaches-9 of 1-4x^3	\lim\:_{x\to\:-9}(1-4x^{3})
integral from 0 to 5 of 2e^x	\int\:_{0}^{5}2e^{x}dx
limit as x approaches 2 of 3x^3+5x	\lim\:_{x\to\:2}(3x^{3}+5x)
limit as x approaches pi/2 of 4sin(x)	\lim\:_{x\to\:\frac{π}{2}}(4\sin(x))
limit as x approaches 1-of (x+2)/(1-x)	\lim\:_{x\to\:1-}(\frac{x+2}{1-x})
tangent of f(x)=5x^2-2x,\at x=3	tangent\:f(x)=5x^{2}-2x,\at\:x=3
derivative of f(x)= 1/2 x^3-2x+3	derivative\:f(x)=\frac{1}{2}x^{3}-2x+3
integral of (12x^3-24x^2+7)/(x^2-2x)	\int\:\frac{12x^{3}-24x^{2}+7}{x^{2}-2x}dx
derivative of (sqrt(s)-3)/(sqrt(s)+7)	derivative\:\frac{\sqrt{s}-3}{\sqrt{s}+7}
limit as x approaches-2 of (-1)/(-x^2+4)	\lim\:_{x\to\:-2}(\frac{-1}{-x^{2}+4})
(dy)/(dx)=4x+(9x^2)/((3x^3+1)^{3/2)}	\frac{dy}{dx}=4x+\frac{9x^{2}}{(3x^{3}+1)^{\frac{3}{2}}}
integral from 0 to 1 of (3x+1)cos(x)	\int\:_{0}^{1}(3x+1)\cos(x)dx
derivative of-9x^2+4x+5	\frac{d}{dx}(-9x^{2}+4x+5)
integral of cot^4(x)	\int\:\cot^{4}(x)dx
(dy)/(dx)=sqrt(y/x)	\frac{dy}{dx}=\sqrt{\frac{y}{x}}
integral of 1/((pix-1))	\int\:\frac{1}{(πx-1)}dx
integral of 4^{ln(x)}	\int\:4^{\ln(x)}dx
(d^2y)/(dx^2)+5(dy)/(dx)+6y=0	\frac{d^{2}y}{dx^{2}}+5\frac{dy}{dx}+6y=0
slope of (1,7),(10,1)	slope\:(1,7),(10,1)
integral of sin(x)x	\int\:\sin(x)xdx
derivative of 2sin(x)+2xcos(x)	derivative\:2\sin(x)+2x\cos(x)
integral of e^ycos(2y)	\int\:e^{y}\cos(2y)dy
limit as x approaches 2 of (2x-25)/(x-2)	\lim\:_{x\to\:2}(\frac{2x-25}{x-2})
implicit (dy)/(dx),xy=y^2	implicit\:\frac{dy}{dx},xy=y^{2}
integral from-infinity to 0 of 1/(6-10x)	\int\:_{-\infty\:}^{0}\frac{1}{6-10x}dx
area \|9x\|,x^2-10	area\:\left\|9x\right\|,x^{2}-10
integral of q^2cos(7q)	\int\:q^{2}\cos(7q)dq
(dy)/(dx)=((y-y^3))/(a^2),y(0)=b	\frac{dy}{dx}=\frac{(y-y^{3})}{a^{2}},y(0)=b
(\partial)/(\partial x)(bxe^{5xy})	\frac{\partial\:}{\partial\:x}(bxe^{5xy})
limit as x approaches (-1)+of 1/(x+1)	\lim\:_{x\to\:(-1)+}(\frac{1}{x+1})
limit as x approaches 2 of (4/x-2)/(x-2)	\lim\:_{x\to\:2}(\frac{\frac{4}{x}-2}{x-2})
(\partial)/(\partial x)(z^2)	\frac{\partial\:}{\partial\:x}(z^{2})
integral of (5x)/(5x^2+2)	\int\:\frac{5x}{5x^{2}+2}dx
derivative of f(x)=e^6+ln(4)	derivative\:f(x)=e^{6}+\ln(4)

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