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Popular Calculus Problems

limit as (x,y) approaches (0,0) of x^3y	\lim\:_{(x,y)\to\:(0,0)}(x^{3}y)
simplify 3/12 x^4+2/6 x^3-x^2+1	simplify\:\frac{3}{12}x^{4}+\frac{2}{6}x^{3}-x^{2}+1
derivative of (6x/((x^2+3)^2))	\frac{d}{dx}(\frac{6x}{(x^{2}+3)^{2}})
tangent of-1/2 x^2-2x+3	tangent\:-\frac{1}{2}x^{2}-2x+3
derivative of 1/x-4/(x^3)	\frac{d}{dx}(\frac{1}{x}-\frac{4}{x^{3}})
derivative of sqrt(30x-x^2)	derivative\:\sqrt{30x-x^{2}}
integral of 1/((3-2x)^2)	\int\:\frac{1}{(3-2x)^{2}}dx
integral of cos(ln(x^2))	\int\:\cos(\ln(x^{2}))dx
3y^'+5y=1	3y^{\prime\:}+5y=1
integral of 2sin(t/2)	\int\:2\sin(\frac{t}{2})dt
derivative of 4cos(x)	derivative\:4\cos(x)
(\partial)/(\partial x)(y-2ln\|y\|+xy)	\frac{\partial\:}{\partial\:x}(y-2\ln\left\|y\right\|+xy)
integral of x*e^{-2x^2}	\int\:x\cdot\:e^{-2x^{2}}dx
derivative of sqrt(ax+b)	\frac{d}{dx}(\sqrt{ax+b})
derivative of (2x^2/(4-x^2))	\frac{d}{dx}(\frac{2x^{2}}{4-x^{2}})
y^{'''}-2y^{''}-4y^'+8y=6xe^{2x}	y^{\prime\:\prime\:\prime\:}-2y^{\prime\:\prime\:}-4y^{\prime\:}+8y=6xe^{2x}
integral of (13)/((x-7)(x+6))	\int\:\frac{13}{(x-7)(x+6)}dx
f(x)=tan(x^2)	f(x)=\tan(x^{2})
limit as x approaches-4 of (x^2)/(4-x)	\lim\:_{x\to\:-4}(\frac{x^{2}}{4-x})
y^{''}-2y^'-3y=4e^{-x},y(0)=4,y^'(0)=-1	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=4e^{-x},y(0)=4,y^{\prime\:}(0)=-1
derivative of x(x^2-5^{1/3})	\frac{d}{dx}(x(x^{2}-5)^{\frac{1}{3}})
integral of y^3sqrt(1+y^4)	\int\:y^{3}\sqrt{1+y^{4}}dy
integral of 29tan^6(x)	\int\:29\tan^{6}(x)dx
derivative of 3e^{2x}	\frac{d}{dx}(3e^{2x})
integral of (20)/(20+e^x)	\int\:\frac{20}{20+e^{x}}dx
integral of 12x^3(3x^4+4)^4	\int\:12x^{3}(3x^{4}+4)^{4}dx
integral of 1/(u^2-9)	\int\:\frac{1}{u^{2}-9}du
integral of (t)	\int\:(t)dt
integral from 0 to 3 of 4e^{-3x}	\int\:_{0}^{3}4e^{-3x}dx
integral of y/((y+4)(2y-1))	\int\:\frac{y}{(y+4)(2y-1)}dy
integral of e^{x+2y}	\int\:e^{x+2y}dy
(\partial)/(\partial y)(yln(y))	\frac{\partial\:}{\partial\:y}(y\ln(y))
integral of sqrt(x^4+1)	\int\:\sqrt{x^{4}+1}dx
integral of e^{9x}cos(2x)	\int\:e^{9x}\cos(2x)dx
2t^2((dx)/(dt))=3tx+x^2	2t^{2}(\frac{dx}{dt})=3tx+x^{2}
f(x)=5sin(x)	f(x)=5\sin(x)
derivative of f(x)=e^{-5x^4}	derivative\:f(x)=e^{-5x^{4}}
area y=4x+2,0,4	area\:y=4x+2,0,4
inverse oflaplace 1/(sqrt(s+1))	inverselaplace\:\frac{1}{\sqrt{s+1}}
tangent of f(x)=6tan(x),\at x= pi/6	tangent\:f(x)=6\tan(x),\at\:x=\frac{π}{6}
xy^'=y+sqrt(x^2-y^2)	xy^{\prime\:}=y+\sqrt{x^{2}-y^{2}}
integral of (1+tan(θ))^5sec^2(θ)	\int\:(1+\tan(θ))^{5}\sec^{2}(θ)dθ
(dy)/(dx)=(y(2x^3-y^3))/(x(2x^3-3y^3))	\frac{dy}{dx}=\frac{y(2x^{3}-y^{3})}{x(2x^{3}-3y^{3})}
derivative of (2x/3)	\frac{d}{dx}(\frac{2x}{3})
integral of sqrt(1+((x^4-1)/(2x^2))^2)	\int\:\sqrt{1+(\frac{x^{4}-1}{2x^{2}})^{2}}dx
integral of x^2arctan(2x^3)	\int\:x^{2}\arctan(2x^{3})dx
integral of 1/(xsqrt(x^2+36))	\int\:\frac{1}{x\sqrt{x^{2}+36}}dx
integral of 1/(uln(u))	\int\:\frac{1}{u\ln(u)}du
integral of 3^{t^2}	\int\:3^{t^{2}}dt
derivative of (3+2x/(sqrt(x)))	\frac{d}{dx}(\frac{3+2x}{\sqrt{x}})
(d^3)/(dx^3)(sqrt(6t+3))	\frac{d^{3}}{dx^{3}}(\sqrt{6t+3})
x^2dx+3y(x-1)dy=0	x^{2}dx+3y(x-1)dy=0
integral of sin(x)+5	\int\:\sin(x)+5dx
integral of (ln(x))/(16)	\int\:\frac{\ln(x)}{16}dx
derivative of (3-4xe^{-2x^2})	\frac{d}{dx}((3-4x)e^{-2x^{2}})
derivative of (x^3-3x^2+4x-5/(x^2))	\frac{d}{dx}(\frac{x^{3}-3x^{2}+4x-5}{x^{2}})
x^2y^{''}+5xy^'+3y=0	x^{2}y^{\prime\:\prime\:}+5xy^{\prime\:}+3y=0
derivative of (7+2x)/(9-8x)	derivative\:\frac{7+2x}{9-8x}
integral of 15e^{-5x}	\int\:15e^{-5x}dx
du= 1/x dx	du=\frac{1}{x}dx
integral of (12e^x-5x^{-2})	\int\:(12e^{x}-5x^{-2})dx
derivative of (x^2-1/(x^2)^6)	\frac{d}{dx}((x^{2}-\frac{1}{x^{2}})^{6})
integral of (sin(2x))/(46+cos^2(x))	\int\:\frac{\sin(2x)}{46+\cos^{2}(x)}dx
derivative of ((x+9))/(sqrt(x))	derivative\:\frac{(x+9)}{\sqrt{x}}
d/(dt)(1/(t^4))	\frac{d}{dt}(\frac{1}{t^{4}})
integral of 8xcos(5x)	\int\:8x\cos(5x)dx
y^{''}+9y^'=1	y^{\prime\:\prime\:}+9y^{\prime\:}=1
limit as x approaches-2 of (2x)/(x^2-4)	\lim\:_{x\to\:-2}(\frac{2x}{x^{2}-4})
f(x)=e^2x	f(x)=e^{2}x
derivative of sec(x^3e^x)	\frac{d}{dx}(\sec(x^{3}e^{x}))
integral of sqrt(2sin(x)+2)	\int\:\sqrt{2\sin(x)+2}dx
integral of (x^2)/(sqrt(5-x^2))	\int\:\frac{x^{2}}{\sqrt{5-x^{2}}}dx
limit as x approaches+pi of (5x)/3	\lim\:_{x\to\:+π}(\frac{5x}{3})
derivative of y=(8x^2+8x+4)/(sqrt(x))	derivative\:y=\frac{8x^{2}+8x+4}{\sqrt{x}}
integral of sqrt(5^x)	\int\:\sqrt{5^{x}}dx
(dy)/(dx)=0.5y-450	\frac{dy}{dx}=0.5y-450
derivative of 2xcos(x)	derivative\:2x\cos(x)
integral of 1/(4+(x-3)^2)	\int\:\frac{1}{4+(x-3)^{2}}dx
integral of (sin(pix))	\int\:(\sin(πx))dx
(\partial)/(\partial y)(5ze^{xyz})	\frac{\partial\:}{\partial\:y}(5ze^{xyz})
(\partial)/(\partial x)(e^{xy}tan(y))	\frac{\partial\:}{\partial\:x}(e^{xy}\tan(y))
limit as h approaches 0 of ((sqrt(18h+1)-1))/h	\lim\:_{h\to\:0}(\frac{(\sqrt{18h+1}-1)}{h})
integral of (sqrt(9x^2+16))/(x^4)	\int\:\frac{\sqrt{9x^{2}+16}}{x^{4}}dx
integral of 2x(x^2-1)	\int\:2x(x^{2}-1)dx
derivative of y=((x^2+3)/(x^2-3))^7	derivative\:y=(\frac{x^{2}+3}{x^{2}-3})^{7}
limit as x approaches 2 of x^2+5x-9	\lim\:_{x\to\:2}(x^{2}+5x-9)
derivative of y=\sqrt[3]{tan(3t)}	derivative\:y=\sqrt[3]{\tan(3t)}
parity cot^2(cos(θ))	parity\:\cot^{2}(\cos(θ))
derivative of arcsin(6x^4)	\frac{d}{dx}(\arcsin(6x^{4}))
derivative of (x^2/3+(5x)/7-8/5)	\frac{d}{dx}(\frac{x^{2}}{3}+\frac{5x}{7}-\frac{8}{5})
tangent of f(x)=5x^3,\at x=-2	tangent\:f(x)=5x^{3},\at\:x=-2
(\partial)/(\partial x)(xarcsin(x)y)	\frac{\partial\:}{\partial\:x}(x\arcsin(x)y)
integral from 0 to pi/2 of xsin(4x)	\int\:_{0}^{\frac{π}{2}}x\sin(4x)dx
taylor \sqrt[4]{x}	taylor\:\sqrt[4]{x}
integral of sqrt(3+s)(s+1)^2	\int\:\sqrt{3+s}(s+1)^{2}ds
derivative of f(x)=ln(25sin^2(x))	derivative\:f(x)=\ln(25\sin^{2}(x))
derivative of y(X)=0.167X	derivative\:y(X)=0.167X
limit as x approaches 0 of x^{9sin(x)}	\lim\:_{x\to\:0}(x^{9\sin(x)})
limit as x approaches 4+of (3x)/(x-4)	\lim\:_{x\to\:4+}(\frac{3x}{x-4})
integral of (u-1)sqrt(u)	\int\:(u-1)\sqrt{u}du

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