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Popular Calculus Problems

d/(da)(1+cos^4(a)-sin^4(a))	\frac{d}{da}(1+\cos^{4}(a)-\sin^{4}(a))
limit as x approaches infinity of (2x)/x	\lim\:_{x\to\:\infty\:}(\frac{2x}{x})
y^{''}+3y^'+2y=e^{3x}sin(2x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=e^{3x}\sin(2x)
implicit (dy)/(dx),y=x^3+2	implicit\:\frac{dy}{dx},y=x^{3}+2
limit as x approaches infinity of e^0	\lim\:_{x\to\:\infty\:}(e^{0})
derivative of 9x^2+6x-2	\frac{d}{dx}(9x^{2}+6x-2)
integral from 0 to infinity of x/(x^4+1)	\int\:_{0}^{\infty\:}\frac{x}{x^{4}+1}dx
limit as x approaches 1 of (x+2)/(1-x)	\lim\:_{x\to\:1}(\frac{x+2}{1-x})
derivative of x^{10}e^x+10	\frac{d}{dx}(x^{10}e^{x}+10)
derivative of f(x)=\sqrt[7]{x}	derivative\:f(x)=\sqrt[7]{x}
d/(dθ)(cos(θ)i+3sin(θ)j)	\frac{d}{dθ}(\cos(θ)i+3\sin(θ)j)
derivative of (e^x/(5x^2+9))	\frac{d}{dx}(\frac{e^{x}}{5x^{2}+9})
integral of (2x+7)/((x-1)^2(x+1))	\int\:\frac{2x+7}{(x-1)^{2}(x+1)}dx
integral from 1 to 2 of 18x^24^{x^3}	\int\:_{1}^{2}18x^{2}4^{x^{3}}dx
integral of (x^2)/(sqrt(x+1))	\int\:\frac{x^{2}}{\sqrt{x+1}}dx
limit as x approaches 0-of 1+e^{1/x}	\lim\:_{x\to\:0-}(1+e^{\frac{1}{x}})
laplacetransform 3t^2+15t+15	laplacetransform\:3t^{2}+15t+15
slope of y=(5x^2-1)^{-3}	slope\:y=(5x^{2}-1)^{-3}
integral from-infinity to 0 of xe^{8x}	\int\:_{-\infty\:}^{0}xe^{8x}dx
derivative of 2x^2-4x	derivative\:2x^{2}-4x
(\partial)/(\partial z)(-z)	\frac{\partial\:}{\partial\:z}(-z)
integral of 1/((x-2)(x-3))	\int\:\frac{1}{(x-2)(x-3)}dx
y^{'''}+3y^{''}-16y^'-48y=0	y^{\prime\:\prime\:\prime\:}+3y^{\prime\:\prime\:}-16y^{\prime\:}-48y=0
integral from-3 to 3 of (18)/(x^2-6x-72)	\int\:_{-3}^{3}\frac{18}{x^{2}-6x-72}dx
(\partial)/(\partial y)((2x)/((2x+3y)^2))	\frac{\partial\:}{\partial\:y}(\frac{2x}{(2x+3y)^{2}})
derivative of f(x)=e^t	derivative\:f(x)=e^{t}
derivative of ln\|sin(x)\|	derivative\:\ln\left\|\sin(x)\right\|
tangent of y=sqrt(2x+1),(4,3)	tangent\:y=\sqrt{2x+1},(4,3)
derivative of 2t^{-1/4}	derivative\:2t^{-\frac{1}{4}}
integral of (x^2)/(e^{x/3)}	\int\:\frac{x^{2}}{e^{\frac{x}{3}}}dx
laplacetransform 5*t	laplacetransform\:5\cdot\:t
integral of 1/(x^2sqrt(x^2+25))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+25}}dx
(\partial)/(\partial y)(sqrt(x/y))	\frac{\partial\:}{\partial\:y}(\sqrt{\frac{x}{y}})
derivative of (4083)/(1+6.22e^{-0.32x)}	derivative\:\frac{4083}{1+6.22e^{-0.32x}}
derivative of f(x)= 4/3 pir^3	derivative\:f(x)=\frac{4}{3}πr^{3}
integral of 24x^2(6-5x^3)^7	\int\:24x^{2}(6-5x^{3})^{7}dx
tangent of f(x)= x/(sqrt(9+x^2)),\at x=0	tangent\:f(x)=\frac{x}{\sqrt{9+x^{2}}},\at\:x=0
y^{''}+2y^'+2y=sin(5t)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(5t)
x^2(dy)/(dx)-2xy=3y^4,y(1)= 1/2	x^{2}\frac{dy}{dx}-2xy=3y^{4},y(1)=\frac{1}{2}
integral of ln(8x)	\int\:\ln(8x)dx
integral of t^{1/3}	\int\:t^{\frac{1}{3}}dt
derivative of sin(5x-3)	derivative\:\sin(5x-3)
integral of 9x^2\sqrt[4]{7+4x^3}	\int\:9x^{2}\sqrt[4]{7+4x^{3}}dx
integral of x^3ln^2(x)	\int\:x^{3}\ln^{2}(x)dx
(\partial)/(\partial x)(ysin(y/x))	\frac{\partial\:}{\partial\:x}(y\sin(\frac{y}{x}))
limit as x approaches-4 of 5x+2	\lim\:_{x\to\:-4}(5x+2)
limit as x approaches-2 of ((3))/((x+2))	\lim\:_{x\to\:-2}(\frac{(3)}{(x+2)})
integral from 0 to 6 of pi/4 (36-y^2)	\int\:_{0}^{6}\frac{π}{4}(36-y^{2})dy
integral from 0 to 1 of 34.6e^{-0.06t}	\int\:_{0}^{1}34.6e^{-0.06t}dt
integral from 0 to 0.15 of x	\int\:_{0}^{0.15}xdx
limit as x approaches 0 of x^9cos(4/x)	\lim\:_{x\to\:0}(x^{9}\cos(\frac{4}{x}))
integral of 1/(xsqrt(49x^4-4))	\int\:\frac{1}{x\sqrt{49x^{4}-4}}dx
y^{''}-y^'-2y=te^{2t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=te^{2t}
derivative of-1/9 (x^{-9}-x^{18})	derivative\:-\frac{1}{9}(x^{-9}-x^{18})
integral of ln(9x+1)	\int\:\ln(9x+1)dx
derivative of 3sqrt(x)+8	\frac{d}{dx}(3\sqrt{x}+8)
t((dy)/(dt))=2te^t-y+6t^2	t(\frac{dy}{dt})=2te^{t}-y+6t^{2}
integral from 0 to 2pi of sin^2(t)	\int\:_{0}^{2π}\sin^{2}(t)dt
(\partial)/(\partial x)(25x^{(3/4)}y^{1/4})	\frac{\partial\:}{\partial\:x}(25x^{(\frac{3}{4})}y^{\frac{1}{4}})
y^'+(2(y-1))/x =0	y^{\prime\:}+\frac{2(y-1)}{x}=0
derivative of sqrt(2x)+2sqrt(x)	\frac{d}{dx}(\sqrt{2x}+2\sqrt{x})
integral from 0 to 1 of sqrt(e^{2x)}	\int\:_{0}^{1}\sqrt{e^{2x}}dx
area 15-x^2,x^2-3	area\:15-x^{2},x^{2}-3
sum from n=1 to infinity of 2e^{-9n}	\sum\:_{n=1}^{\infty\:}2e^{-9n}
integral of te^{8t}	\int\:te^{8t}dt
derivative of f(x)=5x^{-3/5}	derivative\:f(x)=5x^{-\frac{3}{5}}
tangent of y=x^3-7x^2+8x+1	tangent\:y=x^{3}-7x^{2}+8x+1
integral of (64)/(x^3-8x^2)	\int\:\frac{64}{x^{3}-8x^{2}}dx
derivative of (3x^2-x-1/(\sqrt[3]{x)})	\frac{d}{dx}(\frac{3x^{2}-x-1}{\sqrt[3]{x}})
2y^{''}+y^'-4y=0,y(0)=0,y^'(0)=1	2y^{\prime\:\prime\:}+y^{\prime\:}-4y=0,y(0)=0,y^{\prime\:}(0)=1
(\partial)/(\partial y)(xe^{xy})	\frac{\partial\:}{\partial\:y}(x\cdot\:e^{x\cdot\:y})
(\partial)/(\partial x)(-x/((x^2+y^2)))	\frac{\partial\:}{\partial\:x}(-\frac{x}{(x^{2}+y^{2})})
y^{''}-2y^'+y=8e^x	y^{\prime\:\prime\:}-2y^{\prime\:}+y=8e^{x}
limit as x approaches 0+of (ln(x))^2	\lim\:_{x\to\:0+}((\ln(x))^{2})
derivative of sec^2(x)+tan^2(x)	derivative\:\sec^{2}(x)+\tan^{2}(x)
tangent of f(x)=15x-1.86x^2,\at x=a	tangent\:f(x)=15x-1.86x^{2},\at\:x=a
derivative of 7^{x^2}	\frac{d}{dx}(7^{x^{2}})
integral of-3x^2-20x+2000	\int\:-3x^{2}-20x+2000dx
(1+x^2)(dy)/(dx)-(4x^3y)/(1-x^2)=1	(1+x^{2})\frac{dy}{dx}-\frac{4x^{3}y}{1-x^{2}}=1
integral of 3x^2+8x-9	\int\:3x^{2}+8x-9dx
(\partial)/(\partial x)(ln(t+2cx))	\frac{\partial\:}{\partial\:x}(\ln(t+2cx))
derivative of f(x)=ax^b+de^{-cx}	derivative\:f(x)=ax^{b}+de^{-cx}
integral of (4^x-sec^2(x))	\int\:(4^{x}-\sec^{2}(x))dx
integral of 1 (e^{-x}y)	\int\:\frac{d}{1}(e^{-x}y)dx
limit as x approaches 0 of (e^{2x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{2x}-1}{x})
(dy)/(dx)=(x+y^2)/(2y),y(0)=1	\frac{dy}{dx}=\frac{x+y^{2}}{2y},y(0)=1
integral of (x^5)/(x^6-7)	\int\:\frac{x^{5}}{x^{6}-7}dx
derivative of f(x)=arccos(4x^2)	derivative\:f(x)=\arccos(4x^{2})
limit as θ approaches 0 of 1/11	\lim\:_{θ\to\:0}(\frac{1}{11})
laplacetransform sin^2(x)	laplacetransform\:\sin^{2}(x)
limit as x approaches 0+of (2^x)/(3^x-1)	\lim\:_{x\to\:0+}(\frac{2^{x}}{3^{x}-1})
derivative of (x+2sqrt(x)e^x)	\frac{d}{dx}((x+2\sqrt{x})e^{x})
integral of sqrt(16-5x^2)	\int\:\sqrt{16-5x^{2}}dx
slope of (2,5),(-6,-3)	slope\:(2,5),(-6,-3)
derivative of (sin(x)/(2x))	\frac{d}{dx}(\frac{\sin(x)}{2x})
integral from-3 to 3 of sqrt(9-x^2)	\int\:_{-3}^{3}\sqrt{9-x^{2}}dx
integral from-2 to 2 of (x^2-4)^2	\int\:_{-2}^{2}(x^{2}-4)^{2}dx
limit as x approaches 4 of (x-4)/(x+5)	\lim\:_{x\to\:4}(\frac{x-4}{x+5})
integral of (e^{2x}*,x)	\int\:(e^{2x}\cdot\:,x)dx
derivative of (8*sqrt(x))/(x^2+p)	derivative\:\frac{8\cdot\:\sqrt{x}}{x^{2}+p}

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