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Popular Calculus Problems

derivative of ln(1+7x)	\frac{d}{dx}(\ln(1+7x))
derivative of x^2sqrt(4x-9)	\frac{d}{dx}(x^{2}\sqrt{4x-9})
integral of-cos(u)+1/3 cos^3(u)	\int\:-\cos(u)+\frac{1}{3}\cos^{3}(u)du
derivative of (3x^2-10)^{-13}	derivative\:(3x^{2}-10)^{-13}
integral of (-3((9x^2)/2)-4x^3)	\int\:(-3(\frac{9x^{2}}{2})-4x^{3})dx
y^'=(e^t)/(3y^2)	y^{\prime\:}=\frac{e^{t}}{3y^{2}}
integral of 30e^{0.5x}	\int\:30e^{0.5x}dx
x^2y^{''}+xy^'+2y=0	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}+2y=0
integral of 22tan^{21}(x)sec^2(x)	\int\:22\tan^{21}(x)\sec^{2}(x)dx
derivative of 7t^2+sqrt(t^3)	derivative\:7t^{2}+\sqrt{t^{3}}
tangent of f(x)=(1+3x)^9,\at x=0	tangent\:f(x)=(1+3x)^{9},\at\:x=0
derivative of (2x^3-3log_{2}(5-x))	\frac{d}{dx}((2x^{3}-3)\log_{2}(5-x))
tangent of f(x)= 1/(4+3x),\at x=1	tangent\:f(x)=\frac{1}{4+3x},\at\:x=1
(\partial}{\partial v}(\frac{u+v)/3)	\frac{\partial\:}{\partial\:v}(\frac{u+v}{3})
x*(dy)/(dx)-(1+x)y=xy^2	x\cdot\:\frac{dy}{dx}-(1+x)y=xy^{2}
area x^2,0,1	area\:x^{2},0,1
sum from n=0 to infinity of (-1)^nx(x/4)^{2n}	\sum\:_{n=0}^{\infty\:}(-1)^{n}x(\frac{x}{4})^{2n}
derivative of arctan(1+x^2)	\frac{d}{dx}(\arctan(1+x^{2}))
derivative of y=sin(sin(sin(x)))	derivative\:y=\sin(\sin(\sin(x)))
limit as x approaches 5 of xsqrt(29-x^2)	\lim\:_{x\to\:5}(x\sqrt{29-x^{2}})
derivative of e^tsin(3t)	derivative\:e^{t}\sin(3t)
integral of sin^6(2x)cos^3(2x)	\int\:\sin^{6}(2x)\cos^{3}(2x)dx
(\partial)/(\partial x)(xy-z^2+17x^2z)	\frac{\partial\:}{\partial\:x}(xy-z^{2}+17x^{2}z)
tangent of y=-x^2+4x+2,(3,5)	tangent\:y=-x^{2}+4x+2,(3,5)
(\partial)/(\partial x)(x/(y^3))	\frac{\partial\:}{\partial\:x}(\frac{x}{y^{3}})
(\partial)/(\partial x)(4xsin(6x^2y))	\frac{\partial\:}{\partial\:x}(4x\sin(6x^{2}y))
(dy)/(dx)=xy-x	\frac{dy}{dx}=xy-x
y^{''}+2y^'-3y=0	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=0
limit as x approaches a of 1/(sqrt(x))	\lim\:_{x\to\:a}(\frac{1}{\sqrt{x}})
(dy)/(dx)=5y^2	\frac{dy}{dx}=5y^{2}
integral of (2x)/(sqrt(x^2-9))	\int\:\frac{2x}{\sqrt{x^{2}-9}}dx
d/(dt)(-(2cos^2(t)sin(t))/(sin(2t)))	\frac{d}{dt}(-\frac{2\cos^{2}(t)\sin(t)}{\sin(2t)})
integral of 1/(x(y)^2+1)	\int\:\frac{1}{x(y)^{2}+1}dx
limit as x approaches 3 of \sqrt[6]{2-x}	\lim\:_{x\to\:3}(\sqrt[6]{2-x})
integral from 2 to 5 of x^2ln(3x)	\int\:_{2}^{5}x^{2}\ln(3x)dx
x(dy)/(dx)+y=sec(xy)	x\frac{dy}{dx}+y=\sec(xy)
integral of x^7ln(1+x)	\int\:x^{7}\ln(1+x)dx
derivative of 2xe^{x+3}+e^{x+3}x^2	\frac{d}{dx}(2xe^{x+3}+e^{x+3}x^{2})
slope of eln(2x^4+ax^2y^{2+2y^4})	slope\:e\ln(2x^{4}+ax^{2}y^{2+2y^{4}})
derivative of f(x)=sqrt(10x)	derivative\:f(x)=\sqrt{10x}
derivative of (8x^2-x)ln(x)	derivative\:(8x^{2}-x)\ln(x)
sum from n=0 to infinity of ((-1)/3)^{2n}	\sum\:_{n=0}^{\infty\:}(\frac{-1}{3})^{2n}
integral of (23)/(x^3-125)	\int\:\frac{23}{x^{3}-125}dx
derivative of h(x)= 3/(x^2)+5/(x^4)	derivative\:h(x)=\frac{3}{x^{2}}+\frac{5}{x^{4}}
xy^'-2y=7x^2	xy^{\prime\:}-2y=7x^{2}
derivative of (sqrt(9-x^2))/(4x)	derivative\:\frac{\sqrt{9-x^{2}}}{4x}
derivative of f(x)=(x+1)(2x-1)	derivative\:f(x)=(x+1)(2x-1)
integral from 0 to pi/8 of sin^5(4x)	\int\:_{0}^{\frac{π}{8}}\sin^{5}(4x)dx
y^{'''}+y^{''}+3y^'-5y=0	y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}+3y^{\prime\:}-5y=0
integral of (sin(2x))/(2sin(x))	\int\:\frac{\sin(2x)}{2\sin(x)}dx
integral from 4 to infinity of xe^{-3x}	\int\:_{4}^{\infty\:}xe^{-3x}dx
(dy)/(dx)=2xy^2+3x^2y^2,y(1)=-1	\frac{dy}{dx}=2xy^{2}+3x^{2}y^{2},y(1)=-1
integral of (4x+3)/(sqrt(1-x^2))	\int\:\frac{4x+3}{\sqrt{1-x^{2}}}dx
derivative of sin(4x+7x^4+e^{1-x^2})	\frac{d}{dx}(\sin(4x+7x^{4})+e^{1-x^{2}})
integral of (x^2+24x-9)/(x^3-9x)	\int\:\frac{x^{2}+24x-9}{x^{3}-9x}dx
limit as x approaches pi/2 of-cos(x)	\lim\:_{x\to\:\frac{π}{2}}(-\cos(x))
derivative of y=(6x^2+6x+2)/(sqrt(x))	derivative\:y=\frac{6x^{2}+6x+2}{\sqrt{x}}
derivative of (3x^2/(5x^2+7x))	\frac{d}{dx}(\frac{3x^{2}}{5x^{2}+7x})
derivative of 5cos(x)	derivative\:5\cos(x)
(\partial)/(\partial x)(xln(t))	\frac{\partial\:}{\partial\:x}(x\ln(t))
derivative of e^x-e^{-x}	derivative\:e^{x}-e^{-x}
integral of sin(x)*x	\int\:\sin(x)\cdot\:xdx
derivative of sqrt(cos(e^{x^5sin(x))})	\frac{d}{dx}(\sqrt{\cos(e^{x^{5}\sin(x)})})
derivative of-6/(x^3)	derivative\:-\frac{6}{x^{3}}
integral of sqrt(x)arctan(sqrt(x))	\int\:\sqrt{x}\arctan(\sqrt{x})dx
(\partial)/(\partial x)(x^4+12xy^2+2y^4)	\frac{\partial\:}{\partial\:x}(x^{4}+12xy^{2}+2y^{4})
derivative of y=(2x-9)/(3x+7)	derivative\:y=\frac{2x-9}{3x+7}
integral of (7^x)/(sqrt(1-7^{2x))}	\int\:\frac{7^{x}}{\sqrt{1-7^{2x}}}dx
derivative of e^{-3}	\frac{d}{dx}(e^{-3})
derivative of (1-x^{1/2})	\frac{d}{dx}((1-x)^{\frac{1}{2}})
(\partial)/(\partial x)(cos(x)sin(y))	\frac{\partial\:}{\partial\:x}(\cos(x)\sin(y))
y^{''}-10y^'+61y=0	y^{\prime\:\prime\:}-10y^{\prime\:}+61y=0
inverse oflaplace (56s)/(s^2+196)	inverselaplace\:\frac{56s}{s^{2}+196}
(dy)/(dx)=-2xtan(y),y(0)= pi/2	\frac{dy}{dx}=-2x\tan(y),y(0)=\frac{π}{2}
(dx)/(dt)=x(1-0.0004x)	\frac{dx}{dt}=x(1-0.0004x)
integral from 1 to 2 of 9(ln(x))/(x^2)	\int\:_{1}^{2}9\frac{\ln(x)}{x^{2}}dx
integral of 1/(sqrt(x(x+1)))	\int\:\frac{1}{\sqrt{x(x+1)}}dx
tangent of f(x)=sqrt(x-1),(10,3)	tangent\:f(x)=\sqrt{x-1},(10,3)
integral from 0 to 3 of sqrt(4x+5)	\int\:_{0}^{3}\sqrt{4x+5}dx
area x=-3,x=-1,y=x^3+8,y=0	area\:x=-3,x=-1,y=x^{3}+8,y=0
(\partial)/(\partial x)(y^2e^{-x})	\frac{\partial\:}{\partial\:x}(y^{2}e^{-x})
(\partial)/(\partial x)((Ax^c+By^c)^{1/c})	\frac{\partial\:}{\partial\:x}((Ax^{c}+By^{c})^{\frac{1}{c}})
(\partial)/(\partial x)(sqrt((18)/(xy)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{18}{xy}})
integral from 1 to 6 of kx	\int\:_{1}^{6}kxdx
limit as x approaches-2 of (x^2-5)/(2-x)	\lim\:_{x\to\:-2}(\frac{x^{2}-5}{2-x})
derivative of-2x-2	\frac{d}{dx}(-2x-2)
integral from 0 to 1 of 6x	\int\:_{0}^{1}6xdx
area y=e^x,y=x^2-1,x=-1,x=1	area\:y=e^{x},y=x^{2}-1,x=-1,x=1
sum from n=1 to infinity of ne^{6n}	\sum\:_{n=1}^{\infty\:}ne^{6n}
(dy)/(dt)-(3/t)*y=2t^3e^{2t},y(1)=0	\frac{dy}{dt}-(\frac{3}{t})\cdot\:y=2t^{3}e^{2t},y(1)=0
derivative of 7/(sqrt(x))	derivative\:\frac{7}{\sqrt{x}}
y^{''}+y=(x^2+x)sin(x)	y^{\prime\:\prime\:}+y=(x^{2}+x)\sin(x)
derivative of 3sec(x)-7x	derivative\:3\sec(x)-7x
limit as x approaches 8 of (2+8)/(2(8))	\lim\:_{x\to\:8}(\frac{2+8}{2(8)})
sum from n=1 to infinity of 1/(n+2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n+2}
area x^2+y^2=6,x=y^2,y=0	area\:x^{2}+y^{2}=6,x=y^{2},y=0
implicit (dy)/(dx),x^3-3axy+y^3=0	implicit\:\frac{dy}{dx},x^{3}-3axy+y^{3}=0
limit as x approaches pi of sin(7x)	\lim\:_{x\to\:π}(\sin(7x))
integral from-2 to 2 of (3u+1)^2	\int\:_{-2}^{2}(3u+1)^{2}du
derivative of (x^2+2/(x^3+1))	\frac{d}{dx}(\frac{x^{2}+2}{x^{3}+1})

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