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Popular Calculus Problems

tangent of-4cos(x),\at x= pi/2	tangent\:-4\cos(x),\at\:x=\frac{π}{2}
integral of (4x^2)/(x^2+8)	\int\:\frac{4x^{2}}{x^{2}+8}dx
tangent of y=(((x-1))/((x-2)))^2	tangent\:y=(\frac{(x-1)}{(x-2)})^{2}
derivative of-csc(xcot(x))	\frac{d}{dx}(-\csc(x)\cot(x))
(dy)/(dx)+e/pi y=5	\frac{dy}{dx}+\frac{e}{π}y=5
(dy)/(dx)+y^3x+7y=0	\frac{dy}{dx}+y^{3}x+7y=0
y^{''}-3y^'+2y=2t^2+e^t+1	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=2t^{2}+e^{t}+1
sum from n=3 to infinity of (n!)/(2^{n+1)}	\sum\:_{n=3}^{\infty\:}\frac{n!}{2^{n+1}}
(\partial)/(\partial y)(-(y^2)/((x-y)^2))	\frac{\partial\:}{\partial\:y}(-\frac{y^{2}}{(x-y)^{2}})
integral of 7	\int\:7dx
derivative of \sqrt[4]{x}^{ln(x})	\frac{d}{dx}(\sqrt[4]{x}^{\ln(x)})
limit as x approaches-infinity of (-3x^3-4x^2+2)/(5x^3+4x^2-2x)	\lim\:_{x\to\:-\infty\:}(\frac{-3x^{3}-4x^{2}+2}{5x^{3}+4x^{2}-2x})
derivative of e^{-x}(acos(x+bsin(x)))	\frac{d}{dx}(e^{-x}(a\cos(x)+b\sin(x)))
limit as x approaches-infinity of (7x^4-14x^2)/(6x^5+3)	\lim\:_{x\to\:-\infty\:}(\frac{7x^{4}-14x^{2}}{6x^{5}+3})
derivative of sin((sqrt(5)/2 ln(x)))	\frac{d}{dx}(\sin(\frac{\sqrt{5}}{2}\ln(x)))
integral of (sin(kt))/(a+cos(kt))	\int\:\frac{\sin(kt)}{a+\cos(kt)}dt
limit as x approaches 3 of 3x^2+4x-1	\lim\:_{x\to\:3}(3x^{2}+4x-1)
limit as x approaches 0 of (x-2)/(x-2)	\lim\:_{x\to\:0}(\frac{x-2}{x-2})
(\partial)/(\partial y)(e^{-x}sin(y))	\frac{\partial\:}{\partial\:y}(e^{-x}\sin(y))
(\partial)/(\partial x)(x^2+y^2+z^2-9)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+z^{2}-9)
integral of (e^x)/(sqrt(1-64e^{2x))}	\int\:\frac{e^{x}}{\sqrt{1-64e^{2x}}}dx
(\partial)/(\partial x)(1/(ln(x-y)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\ln(x-y)})
sum from n=1 to infinity of 1/(n^{0.3)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{0.3}}
integral of-e^{-y}	\int\:-e^{-y}dy
derivative of f(x)=x^2*sin(x)	derivative\:f(x)=x^{2}\cdot\:\sin(x)
derivative of ((x^3-1)/((x^3+1)))	\frac{d}{dx}(\frac{(x^{3}-1)}{(x^{3}+1)})
tangent of y=0.03x^2+1	tangent\:y=0.03x^{2}+1
integral from 2 to 3 of 1/(4-3x)	\int\:_{2}^{3}\frac{1}{4-3x}dx
integral of-3cos(x)	\int\:-3\cos(x)dx
derivative of x^7(x-12^5)	\frac{d}{dx}(x^{7}(x-12)^{5})
(dy)/(dx)= 1/(x-x^3)	\frac{dy}{dx}=\frac{1}{x-x^{3}}
(\partial)/(\partial x)(2x-3y+5z)	\frac{\partial\:}{\partial\:x}(2x-3y+5z)
integral of 3^{2x}cos^2(3^x)	\int\:3^{2x}\cos^{2}(3^{x})dx
f(x)=sqrt(x)-3	f(x)=\sqrt{x}-3
2x(dy)/(dx)+y=10sqrt(x)	2x\frac{dy}{dx}+y=10\sqrt{x}
integral of e^{-x}sec^2(e^{-x})	\int\:e^{-x}\sec^{2}(e^{-x})dx
d/(dt)(sin(t)cos(t))	\frac{d}{dt}(\sin(t)\cos(t))
(dy)/(dx)=2y+2	\frac{dy}{dx}=2y+2
integral of sin(3x)sec^2(3x)	\int\:\sin(3x)\sec^{2}(3x)dx
(d^2)/(dx^2)(e^{-4x^2})	\frac{d^{2}}{dx^{2}}(e^{-4x^{2}})
(\partial)/(\partial y)((xy^2)/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{xy^{2}}{x+y})
derivative of sec(4x)	derivative\:\sec(4x)
f(x)=cot(x)	f(x)=\cot(x)
integral of 2x+8e^x	\int\:2x+8e^{x}dx
(dy)/(dt)= 4/5 y	\frac{dy}{dt}=\frac{4}{5}y
derivative of (0.09(5^x)/(x^3))	\frac{d}{dx}(\frac{0.09(5^{x})}{x^{3}})
derivative of ln((3x/4))	\frac{d}{dx}(\ln(\frac{3x}{4}))
y^'=(x(x^2+1))/(4y^3)	y^{\prime\:}=\frac{x(x^{2}+1)}{4y^{3}}
integral of 3/(x^4)+4/(x^2)-6/(x^3)	\int\:\frac{3}{x^{4}}+\frac{4}{x^{2}}-\frac{6}{x^{3}}dx
2ty^'+(4+12t^3-120t^2)y=0	2ty^{\prime\:}+(4+12t^{3}-120t^{2})y=0
derivative of y=(5t-1)(6t-3)^{-1}	derivative\:y=(5t-1)(6t-3)^{-1}
tangent of f(x)=x+4e^x	tangent\:f(x)=x+4e^{x}
d/(dt)(acos(wt))	\frac{d}{dt}(a\cos(wt))
derivative of y=2x^2+8x+10	derivative\:y=2x^{2}+8x+10
derivative of (4x^2+5(5x-3))	\frac{d}{dx}((4x^{2}+5)(5x-3))
limit as x approaches 90 of cos(x)	\lim\:_{x\to\:90}(\cos(x))
integral from 0 to 9 of 3/(\sqrt[3]{x-1)}	\int\:_{0}^{9}\frac{3}{\sqrt[3]{x-1}}dx
derivative of f(4)=4x^{5/4}+8x^{3/2}+8x	derivative\:f(4)=4x^{\frac{5}{4}}+8x^{\frac{3}{2}}+8x
(d^2)/(dx^2)(sec(θ))	\frac{d^{2}}{dx^{2}}(\sec(θ))
derivative of-1/(x^3)	derivative\:-\frac{1}{x^{3}}
integral from-infinity to 0 of e^{-3x}	\int\:_{-\infty\:}^{0}e^{-3x}dx
taylor x^3+2x+1,2	taylor\:x^{3}+2x+1,2
y^{''}+64y=0,y(0)=1,y^'(0)=5	y^{\prime\:\prime\:}+64y=0,y(0)=1,y^{\prime\:}(0)=5
derivative of-x^3e^x	\frac{d}{dx}(-x^{3}e^{x})
(\partial)/(\partial x)(xe^{(x^2-y)})	\frac{\partial\:}{\partial\:x}(xe^{(x^{2}-y)})
integral of (x+2)sqrt((3x^2+12x))	\int\:(x+2)\sqrt{(3x^{2}+12x)}dx
(\partial)/(\partial y)(xy^2+ye^{x^2}+5)	\frac{\partial\:}{\partial\:y}(xy^{2}+ye^{x^{2}}+5)
derivative of y=ln(sqrt(x+5))	derivative\:y=\ln(\sqrt{x+5})
limit as x approaches 2 of x^2+6	\lim\:_{x\to\:2}(x^{2}+6)
derivative of ((4x^2+4x+6))/(sqrt(x))	derivative\:\frac{(4x^{2}+4x+6)}{\sqrt{x}}
integral of (x+5)/(2x+3)	\int\:\frac{x+5}{2x+3}dx
integral of te^{-8t}	\int\:te^{-8t}dt
derivative of 5excos(x)	derivative\:5ex\cos(x)
(dy)/(dx)=e^x,x(0)=6	\frac{dy}{dx}=e^{x},x(0)=6
(\partial)/(\partial x)(x^2+y^2+(12-x-y)^2)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+(12-x-y)^{2})
(\partial)/(\partial x)(xye^{-y})	\frac{\partial\:}{\partial\:x}(xye^{-y})
limit as x approaches ln(2) of-4e^{-2x}	\lim\:_{x\to\:\ln(2)}(-4e^{-2x})
integral of 9xe^x	\int\:9xe^{x}dx
y^{''}+4*y=cos(x)	y^{\prime\:\prime\:}+4\cdot\:y=\cos(x)
derivative of x/(x^2+225)	\frac{d}{dx}(\frac{x}{x^{2}+225})
integral from 1 to 4 of x^2-5x+4	\int\:_{1}^{4}x^{2}-5x+4dx
tangent of x^{3/2}+x^{1/2}	tangent\:x^{\frac{3}{2}}+x^{\frac{1}{2}}
limit as x approaches 1 of (sqrt(3-x))/(sqrt(3+x))e^{-x}cos(pix)	\lim\:_{x\to\:1}(\frac{\sqrt{3-x}}{\sqrt{3+x}}e^{-x}\cos(πx))
derivative of (8x^2+6x+8/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+6x+8}{\sqrt{x}})
integral from (sqrt(2))/4 to 1/2 of 1/(x^5sqrt(16x^2-1))	\int\:_{\frac{\sqrt{2}}{4}}^{\frac{1}{2}}\frac{1}{x^{5}\sqrt{16x^{2}-1}}dx
limit as x approaches 0-of x^2*sin(1/x)	\lim\:_{x\to\:0-}(x^{2}\cdot\:\sin(\frac{1}{x}))
integral from-2 to 3 of (33)/(sqrt(3-x))	\int\:_{-2}^{3}\frac{33}{\sqrt{3-x}}dx
integral of-3cos^2(x)sin^2(x)	\int\:-3\cos^{2}(x)\sin^{2}(x)dx
integral of (7x^2)/((36+x^2)^2)	\int\:\frac{7x^{2}}{(36+x^{2})^{2}}dx
(dy)/(dx)=(2x-1)/(sin(y))	\frac{dy}{dx}=\frac{2x-1}{\sin(y)}
(\partial)/(\partial z)(e^{xy}+z)	\frac{\partial\:}{\partial\:z}(e^{xy}+z)
derivative of (x+2^2+(10-3x)^2)	\frac{d}{dx}((x+2)^{2}+(10-3x)^{2})
sum from n=1 to infinity of 1+1/(n+1)	\sum\:_{n=1}^{\infty\:}1+\frac{1}{n+1}
limit as x approaches 0 of ((2-x)^3-8)/x	\lim\:_{x\to\:0}(\frac{(2-x)^{3}-8}{x})
inverse oflaplace 5/(s^2+49)	inverselaplace\:\frac{5}{s^{2}+49}
y(1+x^2)y^'-x(9+y^2)=0	y(1+x^{2})y^{\prime\:}-x(9+y^{2})=0
integral of cos(x)-cos^4(x)	\int\:\cos(x)-\cos^{4}(x)dx
integral of 9x^7e^{-x^4}	\int\:9x^{7}e^{-x^{4}}dx
y^{''}-y^'+4y=2sin(2x)	y^{\prime\:\prime\:}-y^{\prime\:}+4y=2\sin(2x)
integral from 0 to 7 of sqrt(49+x^2)	\int\:_{0}^{7}\sqrt{49+x^{2}}dx

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