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Popular Calculus Problems

derivative of e^{-x}cos(x-e^{-x}sin(x))	\frac{d}{dx}(e^{-x}\cos(x)-e^{-x}\sin(x))
(dy)/(dx)+3y=x^2	\frac{dy}{dx}+3y=x^{2}
integral of (tan^3(θ))/(cos^2(θ))	\int\:\frac{\tan^{3}(θ)}{\cos^{2}(θ)}dθ
tangent of f(x)=x^2-3x+2,\at x=1	tangent\:f(x)=x^{2}-3x+2,\at\:x=1
derivative of (x+9)(9sqrt(x)+7)	derivative\:(x+9)(9\sqrt{x}+7)
integral of xsqrt(7-x^2)	\int\:x\sqrt{7-x^{2}}dx
(\partial)/(\partial x)((2x+y)/((x+2y)^2))	\frac{\partial\:}{\partial\:x}(\frac{2x+y}{(x+2y)^{2}})
f(x)=cos(7x)	f(x)=\cos(7x)
expand (x^2)/(5(1-x))	expand\:\frac{x^{2}}{5(1-x)}
derivative of cos(xt)	\frac{d}{dx}(\cos(xt))
limit as x approaches 0.5 of f(x)	\lim\:_{x\to\:0.5}(f(x))
integral from 1 to 5 of 2/(x^3)	\int\:_{1}^{5}\frac{2}{x^{3}}dx
derivative of arctan(sqrt(x-1))	\frac{d}{dx}(\arctan(\sqrt{x-1}))
derivative of 5/(sqrt(e^x+x))	\frac{d}{dx}(\frac{5}{\sqrt{e^{x}+x}})
limit as x approaches 1+of (x-3)^2	\lim\:_{x\to\:1+}((x-3)^{2})
y^{''}-4y^'+29y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+29y=0
derivative of (2e^x-x^5/(1-3x^5))	\frac{d}{dx}(\frac{2e^{x}-x^{5}}{1-3x^{5}})
derivative of xe^{xy+1}	\frac{d}{dx}(xe^{xy+1})
tangent of f(x)=x^2-3x+2,\at x=2	tangent\:f(x)=x^{2}-3x+2,\at\:x=2
integral of (2x-3)/6	\int\:\frac{2x-3}{6}dx
derivative of ln(x^2)	derivative\:\ln(x^{2})
inverse oflaplace 1/((s+3))	inverselaplace\:\frac{1}{(s+3)}
integral of 1/((2x-3)*(3x^2+x))	\int\:\frac{1}{(2x-3)\cdot\:(3x^{2}+x)}dx
derivative of (x^2/(x^4))	\frac{d}{dx}(\frac{x^{2}}{x^{4}})
derivative of 1/(sqrt(1-x))	\frac{d}{dx}(\frac{1}{\sqrt{1-x}})
integral of coth^2(x)	\int\:\coth^{2}(x)dx
derivative of arccot(x)	derivative\:\arccot(x)
taylor 1/((x^2+4)^3)	taylor\:\frac{1}{(x^{2}+4)^{3}}
limit as x approaches 10 of 5	\lim\:_{x\to\:10}(5)
y^{''}-11y^'+24y=e^{-4t}	y^{\prime\:\prime\:}-11y^{\prime\:}+24y=e^{-4t}
derivative of (4x-3^{1/3})	\frac{d}{dx}((4x-3)^{\frac{1}{3}})
(\partial)/(\partial x)(1/((1+x)^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{(1+x)^{2}})
derivative of (x\|x\|/2)	\frac{d}{dx}(\frac{x\left\|x\right\|}{2})
derivative of (60)/x	derivative\:\frac{60}{x}
integral of 1/(9-x^2)	\int\:\frac{1}{9-x^{2}}dx
integral of e^{-kNx}	\int\:e^{-kNx}dx
derivative of y=Ax^2+Be^{2x}	derivative\:y=Ax^{2}+Be^{2x}
y^'=2xy,y(0)=1	y^{\prime\:}=2xy,y(0)=1
(xy)dx+(x^2+y^2)dy=0	(xy)dx+(x^{2}+y^{2})dy=0
integral of x/(\sqrt[4]{x^2+2)}	\int\:\frac{x}{\sqrt[4]{x^{2}+2}}dx
expand 2(x-6)^3	expand\:2(x-6)^{3}
limit as z approaches 0 of z^3cos(1/z)	\lim\:_{z\to\:0}(z^{3}\cos(\frac{1}{z}))
tangent of f(x)=3sec(x),\at x= pi/3	tangent\:f(x)=3\sec(x),\at\:x=\frac{π}{3}
derivative of cos^3(e^{4x})	derivative\:\cos^{3}(e^{4x})
integral of \sqrt[9]{x^2}+xsqrt(x)	\int\:\sqrt[9]{x^{2}}+x\sqrt{x}dx
tangent of y=x^2-x+7	tangent\:y=x^{2}-x+7
(dx)/(dt)=3xt^2-3t^2	\frac{dx}{dt}=3xt^{2}-3t^{2}
integral from 0 to ln(5) of e^x-e^{-3x}	\int\:_{0}^{\ln(5)}e^{x}-e^{-3x}dx
derivative of (sqrt(x))/(4x+6)	derivative\:\frac{\sqrt{x}}{4x+6}
(\partial)/(\partial x)(xy+4/x+2/y)	\frac{\partial\:}{\partial\:x}(xy+\frac{4}{x}+\frac{2}{y})
derivative of y=ln(2)(x+3)	derivative\:y=\ln(2)(x+3)
taylor sqrt(x),16	taylor\:\sqrt{x},16
derivative of y=-8e^{-2x}-9e^{2x}-5e^x	derivative\:y=-8e^{-2x}-9e^{2x}-5e^{x}
maclaurin 9sin(3x)	maclaurin\:9\sin(3x)
integral of sqrt(1-49x^2)	\int\:\sqrt{1-49x^{2}}dx
integral from 0 to 9 of 2sqrt(x)-(2x)/3	\int\:_{0}^{9}2\sqrt{x}-\frac{2x}{3}dx
derivative of S(t)=(60t^2)/(t^2+150)	derivative\:S(t)=\frac{60t^{2}}{t^{2}+150}
tangent of xsqrt(x^2+60)(2.9)	tangent\:x\sqrt{x^{2}+60}(2.9)
f(x)=e^{10x}	f(x)=e^{10x}
tangent of r=3cos(3θ)	tangent\:r=3\cos(3θ)
(\partial)/(\partial y)(x^2y^2e^{2xy})	\frac{\partial\:}{\partial\:y}(x^{2}y^{2}e^{2xy})
limit as x approaches 1 of (x^2)/2	\lim\:_{x\to\:1}(\frac{x^{2}}{2})
derivative of (20x/(x^2-5))	\frac{d}{dx}(\frac{20x}{x^{2}-5})
(x^{3/2})^'	(x^{\frac{3}{2}})^{\prime\:}
derivative of (3x^2-3/(2x))	\frac{d}{dx}(\frac{3x^{2}-3}{2x})
integral of 2x^2e^x	\int\:2x^{2}e^{x}dx
y^'=1+9x-5y,y(1)=2	y^{\prime\:}=1+9x-5y,y(1)=2
(\partial)/(\partial y)(ln(sqrt(x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\ln(\sqrt{x^{2}+y^{2}}))
integral of (9x^2+5x+9)/((x^2+1)^2)	\int\:\frac{9x^{2}+5x+9}{(x^{2}+1)^{2}}dx
maclaurin ln(4+x^2)	maclaurin\:\ln(4+x^{2})
integral from 1 to 2 of 15sqrt(4x^2-3)	\int\:_{1}^{2}15\sqrt{4x^{2}-3}dx
derivative of f(x)=x^2(1-6x)	derivative\:f(x)=x^{2}(1-6x)
sum from n=0 to infinity of 7(-1/7)^n	\sum\:_{n=0}^{\infty\:}7(-\frac{1}{7})^{n}
(\partial)/(\partial x)(-xsin(y)+e^x)	\frac{\partial\:}{\partial\:x}(-x\sin(y)+e^{x})
y^{''}-4y^'+2y=0,y(0)=0,y^'(0)=7	y^{\prime\:\prime\:}-4y^{\prime\:}+2y=0,y(0)=0,y^{\prime\:}(0)=7
limit as x approaches infinity of 1/8	\lim\:_{x\to\:\infty\:}(\frac{1}{8})
tangent of f(x)= 3/(4x+1),(-1,-1)	tangent\:f(x)=\frac{3}{4x+1},(-1,-1)
derivative of f(x)=((x^2+1))/((x^2-1))	derivative\:f(x)=\frac{(x^{2}+1)}{(x^{2}-1)}
area x+y^2=20,x+y=0	area\:x+y^{2}=20,x+y=0
derivative of f(x)=x^2-3x+4	derivative\:f(x)=x^{2}-3x+4
limit as x approaches-8 of 4x-2	\lim\:_{x\to\:-8}(4x-2)
(\partial)/(\partial y)(x/((y+z)))	\frac{\partial\:}{\partial\:y}(\frac{x}{(y+z)})
(\partial)/(\partial x)(xln(x))	\frac{\partial\:}{\partial\:x}(x\ln(x))
derivative of 2x+(200/x)	\frac{d}{dx}(2x+\frac{200}{x})
derivative of f(x)= 32/0	derivative\:f(x)=\frac{32}{0}
derivative of ln^2(x+2ln(x))	\frac{d}{dx}(\ln^{2}(x)+2\ln(x))
integral of 1/(x^2(sqrt(x^2-16)))	\int\:\frac{1}{x^{2}(\sqrt{x^{2}-16})}dx
integral of ln(cos(x))tan(x)	\int\:\ln(\cos(x))\tan(x)dx
(dy)/(dx)=(-24)/((2x+9)^3)	\frac{dy}{dx}=\frac{-24}{(2x+9)^{3}}
(\partial)/(\partial y)(e^{-y}cos(pix))	\frac{\partial\:}{\partial\:y}(e^{-y}\cos(πx))
integral of (x^2+e^x-sin(x))	\int\:(x^{2}+e^{x}-\sin(x))dx
(sqrt(3x))^'	(\sqrt{3x})^{\prime\:}
integral of 4tan^2(x)sec^2(x)	\int\:4\tan^{2}(x)\sec^{2}(x)dx
area y=3x,y= 5/7 x,y=54-x^2	area\:y=3x,y=\frac{5}{7}x,y=54-x^{2}
integral of arcsin(1/x)	\int\:\arcsin(\frac{1}{x})dx
taylor f(x)=8.8sqrt(x)	taylor\:f(x)=8.8\sqrt{x}
derivative of e^{2x}x(acos(x+bsin(x)))	\frac{d}{dx}(e^{2x}x(a\cos(x)+b\sin(x)))
y^{''}+3y^'-4y=-8e^xcos(2x)	y^{\prime\:\prime\:}+3y^{\prime\:}-4y=-8e^{x}\cos(2x)
derivative of 1/2 x-1/10	\frac{d}{dx}(\frac{1}{2}x-\frac{1}{10})
(\partial)/(\partial u)(sqrt(u^2+v^2+w^2))	\frac{\partial\:}{\partial\:u}(\sqrt{u^{2}+v^{2}+w^{2}})

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