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Popular Calculus Problems

derivative of cos(θ^2)	derivative\:\cos(θ^{2})
integral of x(x^2+4)^5	\int\:x(x^{2}+4)^{5}dx
(\partial)/(\partial x)(e^{yx})	\frac{\partial\:}{\partial\:x}(e^{yx})
integral of (e^{2y})/(e^y-1)	\int\:\frac{e^{2y}}{e^{y}-1}dy
integral of sec^3(5x)	\int\:\sec^{3}(5x)dx
derivative of y=arcsin(x)	derivative\:y=\arcsin(x)
integral of x/((x^2-1)^{1/2)}	\int\:\frac{x}{(x^{2}-1)^{\frac{1}{2}}}dx
derivative of 2z	derivative\:2z
(\partial)/(\partial y)(x^2*e^{-2y})	\frac{\partial\:}{\partial\:y}(x^{2}\cdot\:e^{-2y})
implicit (dy)/(dx),y=x^pi	implicit\:\frac{dy}{dx},y=x^{π}
area y=\sqrt[3]{x},y= 1/x ,x=27	area\:y=\sqrt[3]{x},y=\frac{1}{x},x=27
ty^'+t^2+ty-y=0	ty^{\prime\:}+t^{2}+ty-y=0
limit as h approaches 0 of ((1+h)^9-1)/h	\lim\:_{h\to\:0}(\frac{(1+h)^{9}-1}{h})
derivative of x^3+6x^2	\frac{d}{dx}(x^{3}+6x^{2})
5sqrt(xy)((dy)/(dx))=3	5\sqrt{xy}(\frac{dy}{dx})=3
integral from 0 to 2 of xsqrt(1+2x^2)	\int\:_{0}^{2}x\sqrt{1+2x^{2}}dx
integral of 3+tan^2(x)	\int\:3+\tan^{2}(x)dx
derivative of 3csc(x)	derivative\:3\csc(x)
integral of cos^4(11x)	\int\:\cos^{4}(11x)dx
integral of (e^{2x}+1)/(e^x)	\int\:\frac{e^{2x}+1}{e^{x}}dx
derivative of 1-cos(x)	derivative\:1-\cos(x)
derivative of (5+sin(x))/(5x+cos(x))	derivative\:\frac{5+\sin(x)}{5x+\cos(x)}
integral of 1/(yln^2(y))	\int\:\frac{1}{y\ln^{2}(y)}dy
integral of (sin(x)-x)/(x^3)	\int\:\frac{\sin(x)-x}{x^{3}}dx
y^'=4(y^2+1)	y^{\prime\:}=4(y^{2}+1)
limit as x approaches infinity of 1/x-5	\lim\:_{x\to\:\infty\:}(\frac{1}{x}-5)
limit as x approaches 3 of 4/(x^2+2x+3)	\lim\:_{x\to\:3}(\frac{4}{x^{2}+2x+3})
derivative of 14-1/2 x^{-3}	\frac{d}{dx}(14-\frac{1}{2}x^{-3})
derivative of y=arcsin(8x+1)	derivative\:y=\arcsin(8x+1)
derivative of cos^2(2x^4-4)	\frac{d}{dx}(\cos^{2}(2x^{4}-4))
integral of (sec^4(x))/(tan^3(x))	\int\:\frac{\sec^{4}(x)}{\tan^{3}(x)}dx
integral of (x-5)cos(x)	\int\:(x-5)\cos(x)dx
limit as x approaches 2 of ((x-2))/(x-2)	\lim\:_{x\to\:2}(\frac{(x-2)}{x-2})
integral of 3/(x^2-1)	\int\:\frac{3}{x^{2}-1}dx
integral of θsec^2(θ)	\int\:θ\sec^{2}(θ)dθ
maclaurin sin(x^4)	maclaurin\:\sin(x^{4})
integral from 0 to 7 of (3t)/((t-8)^2)	\int\:_{0}^{7}\frac{3t}{(t-8)^{2}}dt
tangent of f(x)= 2/(3x+5),\at a=-1	tangent\:f(x)=\frac{2}{3x+5},\at\:a=-1
integral from 0 to 4 of pi(4x-x^2)	\int\:_{0}^{4}π(4x-x^{2})dx
derivative of f(x)=\sqrt[4]{x^5}-3/(x^2)	derivative\:f(x)=\sqrt[4]{x^{5}}-\frac{3}{x^{2}}
maclaurin xsin(-2x)pi	maclaurin\:x\sin(-2x)π
9y^{''}-7y=0	9y^{\prime\:\prime\:}-7y=0
derivative of (40/(x+1))	\frac{d}{dx}(\frac{40}{x+1})
inverse oflaplace ((s+2))/(s^2+4)	inverselaplace\:\frac{(s+2)}{s^{2}+4}
integral of 1tan^2(x)	\int\:1\tan^{2}(x)dx
derivative of g(x)=14(1.7^x)	derivative\:g(x)=14(1.7^{x})
(\partial)/(\partial y)(e^{3x})	\frac{\partial\:}{\partial\:y}(e^{3x})
limit as x approaches 2-of x/(\|x\|)	\lim\:_{x\to\:2-}(\frac{x}{\left\|x\right\|})
integral of (x^2-1)/(x^2-4)	\int\:\frac{x^{2}-1}{x^{2}-4}dx
limit as x approaches infinity of (3e^x)/(9+2e^{5x)}	\lim\:_{x\to\:\infty\:}(\frac{3e^{x}}{9+2e^{5x}})
y^'+3y=5	y^{\prime\:}+3y=5
limit as x approaches infinity of (x^3+2x+4)/(e^{1x)+1}	\lim\:_{x\to\:\infty\:}(\frac{x^{3}+2x+4}{e^{1x}+1})
normal of y=4x^2-6x,\at x=2	normal\:y=4x^{2}-6x,\at\:x=2
(dy)/(dx)=(y^2+x^2)/(yx)	\frac{dy}{dx}=\frac{y^{2}+x^{2}}{yx}
integral of cos^9(x)	\int\:\cos^{9}(x)dx
integral of (8x^3-3x^2+8)	\int\:(8x^{3}-3x^{2}+8)dx
derivative of x^5e^{6x}	\frac{d}{dx}(x^{5}e^{6x})
limit as x approaches infinity of 2/x	\lim\:_{x\to\:\infty\:}(\frac{2}{x})
derivative of-2cos(3x)	\frac{d}{dx}(-2\cos(3x))
limit as x approaches 0+of x/(3x)-7x	\lim\:_{x\to\:0+}(\frac{x}{3x}-7x)
integral of 3/91 x^2	\int\:\frac{3}{91}x^{2}dx
(\partial)/(\partial x)((x+y)/(x+z))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{x+z})
(dx)/(dt)=-x/(10)+1/(10e^{\frac{t){10}}}	\frac{dx}{dt}=-\frac{x}{10}+\frac{1}{10e^{\frac{t}{10}}}
ty^'-y=3t^2cos(2t)	ty^{\prime\:}-y=3t^{2}\cos(2t)
integral of x(8x+5)^8	\int\:x(8x+5)^{8}dx
integral of x-1/2	\int\:x-\frac{1}{2}dx
y^{''}+3y^'+2y= 1/(2+e^x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\frac{1}{2+e^{x}}
tangent of f(x)=(1+4x)^{3/2},\at x=2	tangent\:f(x)=(1+4x)^{\frac{3}{2}},\at\:x=2
derivative of y=x^2-5x-3	derivative\:y=x^{2}-5x-3
derivative of (tan^2(x)/2)	\frac{d}{dx}(\frac{\tan^{2}(x)}{2})
derivative of e^{3x+3}	\frac{d}{dx}(e^{3x+3})
integral of 1/(2x^2-5x+7)	\int\:\frac{1}{2x^{2}-5x+7}dx
integral of (x+1)e^{x^2+2x}	\int\:(x+1)e^{x^{2}+2x}dx
derivative of g(t)=t^2-7/(t^3)	derivative\:g(t)=t^{2}-\frac{7}{t^{3}}
limit as x approaches 0 of ((343+x)^{1/3}-7)/x	\lim\:_{x\to\:0}(\frac{(343+x)^{\frac{1}{3}}-7}{x})
(\partial)/(\partial x)(-2x^2)	\frac{\partial\:}{\partial\:x}(-2x^{2})
laplacetransform 1+sin(pi*t)	laplacetransform\:1+\sin(π\cdot\:t)
derivative of 6sqrt(2)x	\frac{d}{dx}(6\sqrt{2}x)
derivative of e^{-2/x}	derivative\:e^{-\frac{2}{x}}
derivative of xe^{5x}	derivative\:xe^{5x}
integral of (e^{sqrt(x+1)})/(sqrt(x+1))	\int\:\frac{e^{\sqrt{x+1}}}{\sqrt{x+1}}dx
derivative of f(x)=(x^2)/(9+8x)	derivative\:f(x)=\frac{x^{2}}{9+8x}
integral of x^5*e^{x^3}	\int\:x^{5}\cdot\:e^{x^{3}}dx
integral of x/(x^2sqrt(x^2-16))	\int\:\frac{x}{x^{2}\sqrt{x^{2}-16}}dx
derivative of tan(5x^2)	\frac{d}{dx}(\tan(5x^{2}))
(\partial)/(\partial x)(4ln(x))	\frac{\partial\:}{\partial\:x}(4\ln(x))
partialfraction (x^2)/(x^2-4)	partialfraction\:\frac{x^{2}}{x^{2}-4}
roots ax*e^{bx}	roots\:ax\cdot\:e^{bx}
integral of (3x^2-8x+2)	\int\:(3x^{2}-8x+2)dx
simplify 3/(cos^2(3x+5))	simplify\:\frac{3}{\cos^{2}(3x+5)}
d/(dt)((t+3)^{2/3}(2t^2-3)^3)	\frac{d}{dt}((t+3)^{\frac{2}{3}}(2t^{2}-3)^{3})
derivative of f(t)=5t-9t^2	derivative\:f(t)=5t-9t^{2}
(\partial)/(\partial x)(x^2-xy+y^2+3x-2y+1)	\frac{\partial\:}{\partial\:x}(x^{2}-xy+y^{2}+3x-2y+1)
y^2=2xyy^'	y^{2}=2xyy^{\prime\:}
limit as x approaches-1 of 2	\lim\:_{x\to\:-1}(2)
(\partial)/(\partial x)(x/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}})
y^'+3/x y= 1/(x^2)	y^{\prime\:}+\frac{3}{x}y=\frac{1}{x^{2}}
derivative of 4-3sin(3x)	\frac{d}{dx}(4-3\sin(3x))
y^{''}+9y=-sin(3x),y(0)=0,y^'(0)= 1/6	y^{\prime\:\prime\:}+9y=-\sin(3x),y(0)=0,y^{\prime\:}(0)=\frac{1}{6}
taylor x^3,0	taylor\:x^{3},0

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