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Popular Calculus Problems

derivative of f(t)=t^2-pi^2	derivative\:f(t)=t^{2}-π^{2}
limit as x approaches 0+of 8/(5x^{1/5)}	\lim\:_{x\to\:0+}(\frac{8}{5x^{\frac{1}{5}}})
derivative of (x-sqrt(x)/(x^{1/6)})	\frac{d}{dx}(\frac{x-\sqrt{x}}{x^{\frac{1}{6}}})
(dx)/(dt)=e^xsin(t)	\frac{dx}{dt}=e^{x}\sin(t)
derivative of e^{2sin(3v)}	derivative\:e^{2\sin(3v)}
derivative of sqrt(2-2x)	derivative\:\sqrt{2-2x}
derivative of f(x)=(x-ln(1+x))/(x^2)	derivative\:f(x)=\frac{x-\ln(1+x)}{x^{2}}
integral of 63sec^4(θ)tan^6(θ)	\int\:63\sec^{4}(θ)\tan^{6}(θ)dθ
derivative of xy+ln(x/y)	\frac{d}{dx}(xy+\ln(\frac{x}{y}))
y^{''}-6y^'+9y=0,y(0)=2,y^'(0)= 25/3	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=2,y^{\prime\:}(0)=\frac{25}{3}
integral of 2y-5	\int\:2y-5dy
limit as x approaches+3-of f(x)	\lim\:_{x\to\:+3-}(f(x))
integral of (2/(\sqrt[5]{x)}-1)^2	\int\:(\frac{2}{\sqrt[5]{x}}-1)^{2}dx
integral of x(x-2)	\int\:x(x-2)dx
derivative of ((4x^2+8x+4))/(sqrt(x))	derivative\:\frac{(4x^{2}+8x+4)}{\sqrt{x}}
integral of x^3e^{2x^4}	\int\:x^{3}e^{2x^{4}}dx
tangent of y=e^x(x^2-3)	tangent\:y=e^{x}(x^{2}-3)
integral of sin(8pit)	\int\:\sin(8πt)dt
derivative of xln(2x+3)	\frac{d}{dx}(x\ln(2x+3))
xy^'=y+2sqrt(xy)	xy^{\prime\:}=y+2\sqrt{xy}
derivative of (1+x)^2	derivative\:(1+x)^{2}
integral of 3/(\sqrt[3]{x)(1+x)}	\int\:\frac{3}{\sqrt[3]{x}(1+x)}dx
integral of (sqrt(x)-1)^2(1+x^{1/2})^2	\int\:(\sqrt{x}-1)^{2}(1+x^{\frac{1}{2}})^{2}dx
derivative of arctan(16x)	derivative\:\arctan(16x)
y^'=(y+sqrt(x^2+y^2))/x	y^{\prime\:}=\frac{y+\sqrt{x^{2}+y^{2}}}{x}
derivative of y=2x^3+3x^2-12x+6	derivative\:y=2x^{3}+3x^{2}-12x+6
integral of 1/(9x^2)	\int\:\frac{1}{9x^{2}}dx
(\partial)/(\partial x)(x^2yz^3(x-10y))	\frac{\partial\:}{\partial\:x}(x^{2}yz^{3}(x-10y))
integral of arcsec(4x)	\int\:\arcsec(4x)dx
derivative of (e^tx+1)dx	derivative\:(e^{t}x+1)dx
(\partial)/(\partial x)(2y+x)	\frac{\partial\:}{\partial\:x}(2y+x)
integral of sqrt(y)-y	\int\:\sqrt{y}-ydy
derivative of (13)/(ln(x))	derivative\:\frac{13}{\ln(x)}
tangent of y= 1/(sqrt(x)),\at x=4	tangent\:y=\frac{1}{\sqrt{x}},\at\:x=4
limit as x approaches-2 of 3x+x^2	\lim\:_{x\to\:-2}(3x+x^{2})
(\partial)/(\partial x)(2(x+3y))	\frac{\partial\:}{\partial\:x}(2(x+3y))
limit as x approaches 0+of 1/(x^{2/3)}	\lim\:_{x\to\:0+}(\frac{1}{x^{\frac{2}{3}}})
derivative of (x+2/(9x^2e^x))	\frac{d}{dx}(\frac{x+2}{9x^{2}e^{x}})
(\partial)/(\partial x)(x^2+ln(y))	\frac{\partial\:}{\partial\:x}(x^{2}+\ln(y))
(\partial}{\partial s}(\frac{r+s)/t)	\frac{\partial\:}{\partial\:s}(\frac{r+s}{t})
derivative of sin(9ln(x))	derivative\:\sin(9\ln(x))
y^'=3y-1	y^{\prime\:}=3y-1
inverse oflaplace (3s+3)/((s+4)^2)	inverselaplace\:\frac{3s+3}{(s+4)^{2}}
integral of 1/(sqrt(441-x^2))	\int\:\frac{1}{\sqrt{441-x^{2}}}dx
derivative of cos(x+x)	\frac{d}{dx}(\cos(x)+x)
derivative of 3x^2-12x	\frac{d}{dx}(3x^{2}-12x)
integral of ln(12x)	\int\:\ln(12x)dx
2xyy^'=4x^2+3y^2	2xyy^{\prime\:}=4x^{2}+3y^{2}
integral from 0 to 1 of integral from-1 to \|x\|^{-1 of}(x+y)^2	\int\:_{0}^{1}\int\:_{-1}^{\left\|x\right\|^{-1}}(x+y)^{2}dydx
integral of 2xe^{x^2+3}	\int\:2xe^{x^{2}+3}dx
limit as x approaches 8 of (x-8)/(x^{1/3)-2}	\lim\:_{x\to\:8}(\frac{x-8}{x^{\frac{1}{3}}-2})
derivative of sqrt(4x^3)	\frac{d}{dx}(\sqrt{4x^{3}})
derivative of x+x^{-1}	\frac{d}{dx}(x+x^{-1})
limit as x approaches+0 of (3x)/(xe^x)	\lim\:_{x\to\:+0}(\frac{3x}{xe^{x}})
(\partial)/(\partial y)(sqrt(x^3y-y^4))	\frac{\partial\:}{\partial\:y}(\sqrt{x^{3}y-y^{4}})
derivative of arcsin(9x^4)	\frac{d}{dx}(\arcsin(9x^{4}))
y^{''}=2t^2	y^{\prime\:\prime\:}=2t^{2}
d/(d{y)}((6{x}+{y})/(8{z)-5{y}})	\frac{d}{d{y}}(\frac{6{x}+{y}}{8{z}-5{y}})
derivative of-4ln(x)	\frac{d}{dx}(-4\ln(x))
(\partial)/(\partial x)(4+cos(0.4x-t))	\frac{\partial\:}{\partial\:x}(4+\cos(0.4x-t))
derivative of (e^x)^3	derivative\:(e^{x})^{3}
(4x^3+3x^2+3y-1)dx+(3x+2y+1)dy=0	(4x^{3}+3x^{2}+3y-1)dx+(3x+2y+1)dy=0
limit as x approaches infinity of (5e^{-3x}+2)/(e^{-5x)+4}	\lim\:_{x\to\:\infty\:}(\frac{5e^{-3x}+2}{e^{-5x}+4})
derivative of 2^{2-x^4}	\frac{d}{dx}(2^{2-x^{4}})
integral of (e^{(x^2)/2})/(x^2)	\int\:\frac{e^{\frac{x^{2}}{2}}}{x^{2}}dx
derivative of 3ln(x^2+1)	\frac{d}{dx}(3\ln(x^{2}+1))
integral of (5x+3)\sqrt[3]{5x^2+6x}	\int\:(5x+3)\sqrt[3]{5x^{2}+6x}dx
area sqrt(x+2), 1/(1+x),x=2	area\:\sqrt{x+2},\frac{1}{1+x},x=2
y^{''}+7y^'+10y=4te^{4t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=4te^{4t}
tangent of f(x)=10x^2,\at x=-2	tangent\:f(x)=10x^{2},\at\:x=-2
derivative of f(x)=sqrt((2x+1)/(2x^2+1))	derivative\:f(x)=\sqrt{\frac{2x+1}{2x^{2}+1}}
derivative of (10)/(x^3)	derivative\:\frac{10}{x^{3}}
sum from n=1 to infinity of (cos(1.4))^n	\sum\:_{n=1}^{\infty\:}(\cos(1.4))^{n}
derivative of (x^2+1^{1/x})	\frac{d}{dx}((x^{2}+1)^{\frac{1}{x}})
integral of (4x)/(x^3+x^2+x+1)	\int\:\frac{4x}{x^{3}+x^{2}+x+1}dx
integral from 0 to t of t^2e^{-5t}	\int\:_{0}^{t}t^{2}e^{-5t}dt
(\partial)/(\partial x)(\|xy\|)	\frac{\partial\:}{\partial\:x}(\left\|xy\right\|)
d/(dt)(e^{-6t})	\frac{d}{dt}(e^{-6t})
y^'-6+y/((4(x+250)))=0,y(0)=70	y^{\prime\:}-6+\frac{y}{(4(x+250))}=0,y(0)=70
integral of 2xsec(4x^2)	\int\:2x\sec(4x^{2})dx
integral from 0 to 1 of (e^x)/(16-e^{2x)}	\int\:_{0}^{1}\frac{e^{x}}{16-e^{2x}}dx
integral of-sin(nx)	\int\:-\sin(nx)dx
integral from 0 to 1/2 of arcsin(2y)	\int\:_{0}^{\frac{1}{2}}\arcsin(2y)dy
derivative of 9sin(θ)cos(θ)	derivative\:9\sin(θ)\cos(θ)
derivative of xln(x-1)	\frac{d}{dx}(x\ln(x)-1)
integral of t^2e^{-2t}	\int\:t^{2}e^{-2t}dt
integral of ((e^{2x}-1))/((e^x+e^{-x))}	\int\:\frac{(e^{2x}-1)}{(e^{x}+e^{-x})}dx
derivative of (2x/(3x^2-12))	\frac{d}{dx}(\frac{2x}{3x^{2}-12})
tangent of (x^3+4)(3x^2-4x+2)	tangent\:(x^{3}+4)(3x^{2}-4x+2)
inverse oflaplace 3t^2+15t+19	inverselaplace\:3t^{2}+15t+19
(dy)/(dx)=(xy-y)/(y+1)	\frac{dy}{dx}=\frac{xy-y}{y+1}
limit as x approaches infinity of x/(3^{2x+1)}	\lim\:_{x\to\:\infty\:}(\frac{x}{3^{2x+1}})
derivative of x/(arctan(x))	\frac{d}{dx}(\frac{x}{\arctan(x)})
implicit (dy)/(dx),ysin(1/y)=1-xy	implicit\:\frac{dy}{dx},y\sin(\frac{1}{y})=1-xy
(\partial)/(\partial y)(xye^x)	\frac{\partial\:}{\partial\:y}(xye^{x})
integral of sqrt(x)-x^3	\int\:\sqrt{x}-x^{3}dx
integral of (1+4x)^3	\int\:(1+4x)^{3}dx
derivative of log_{8}(sqrt(x))	\frac{d}{dx}(\log_{8}(\sqrt{x}))
integral of cot^6(2t)	\int\:\cot^{6}(2t)dt
integral of 7e^{-0.5x}	\int\:7e^{-0.5x}dx

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