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Popular Calculus Problems

derivative of ln\|ln(x\|)	\frac{d}{dx}(\ln\left\|\ln(x)\right\|)
derivative of y=x^{(1/(ln(x)))}	derivative\:y=x^{(\frac{1}{\ln(x)})}
integral of sin^5(x)*cos^5(x)	\int\:\sin^{5}(x)\cdot\:\cos^{5}(x)dx
limit as x approaches 0 of 7/(cos(x))	\lim\:_{x\to\:0}(\frac{7}{\cos(x)})
(dx)/(dy)+1/(y^2)x= 1/(y^2)	\frac{dx}{dy}+\frac{1}{y^{2}}x=\frac{1}{y^{2}}
derivative of f(x)=x^2(4x^3-1)	derivative\:f(x)=x^{2}(4x^{3}-1)
integral of (sqrt(x^2-36))/(x^4)	\int\:\frac{\sqrt{x^{2}-36}}{x^{4}}dx
integral from 1 to 2 of (-2x+6)	\int\:_{1}^{2}(-2x+6)dx
tangent of 3x^2+2	tangent\:3x^{2}+2
derivative of y=(x^2+3x)2	derivative\:y=(x^{2}+3x)2
(\partial)/(\partial x)(5x^2+y^2+9)	\frac{\partial\:}{\partial\:x}(5x^{2}+y^{2}+9)
integral of (cos^2(θ))^2	\int\:(\cos^{2}(θ))^{2}dθ
(\partial)/(\partial x)(e^{-6t}(x+3t))	\frac{\partial\:}{\partial\:x}(e^{-6t}(x+3t))
(d^2}{dx^2}(\frac{4x^3+6)/x)	\frac{d^{2}}{dx^{2}}(\frac{4x^{3}+6}{x})
inverse oflaplace s/(s^2-4s+5)	inverselaplace\:\frac{s}{s^{2}-4s+5}
integral from t to 2 of 1/(sqrt(x-1))	\int\:_{t}^{2}\frac{1}{\sqrt{x-1}}dx
derivative of-(1/x)	\frac{d}{dx}(-(\frac{1}{x}))
integral of 2/((x-1)^2)	\int\:\frac{2}{(x-1)^{2}}dx
derivative of cos(sin(x))	derivative\:\cos(\sin(x))
(\partial}{\partial x}(e^{\frac{-2y)/x})	\frac{\partial\:}{\partial\:x}(e^{\frac{-2y}{x}})
derivative of (e^{2x}/(x^4))	\frac{d}{dx}(\frac{e^{2x}}{x^{4}})
g(f)=f^8	g(f)=f^{8}
integral of 1/(sqrt(x+5))	\int\:\frac{1}{\sqrt{x+5}}dx
laplacetransform e^{-3t}+3	laplacetransform\:e^{-3t}+3
integral of (-t)/((t+1)-(sqrt(t+1)))	\int\:\frac{-t}{(t+1)-(\sqrt{t+1})}dt
(\partial)/(\partial t)((3y^2-t^2)/(y^5))	\frac{\partial\:}{\partial\:t}(\frac{3y^{2}-t^{2}}{y^{5}})
limit as x approaches 0 of ((3^x-1))/x	\lim\:_{x\to\:0}(\frac{(3^{x}-1)}{x})
integral from 0 to 6 of pi(36x^2-x^4)	\int\:_{0}^{6}π(36x^{2}-x^{4})dx
limit as x approaches 0 of (ln(x))^x	\lim\:_{x\to\:0}((\ln(x))^{x})
integral of x/(sqrt(x-3))	\int\:\frac{x}{\sqrt{x-3}}dx
integral of 1/2 cos(sqrt(x))	\int\:\frac{1}{2}\cos(\sqrt{x})dx
derivative of (3x/(x^3+7x-5))	\frac{d}{dx}(\frac{3x}{x^{3}+7x-5})
derivative of f(x)=log_{2}(1-3x)	derivative\:f(x)=\log_{2}(1-3x)
derivative of sin(2x+pi)	derivative\:\sin(2x+π)
y^{''}+4y^'+3y=4e^x,y(0)=0,y^'(0)=2	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=4e^{x},y(0)=0,y^{\prime\:}(0)=2
integral of 3x^2(x^3+1)^2	\int\:3x^{2}(x^{3}+1)^{2}dx
(\partial)/(\partial x)(cos(y)+ye^x)	\frac{\partial\:}{\partial\:x}(\cos(y)+ye^{x})
integral of (16)/(x^2sqrt(16-x^2))	\int\:\frac{16}{x^{2}\sqrt{16-x^{2}}}dx
y^'=-y/((x+2/y))	y^{\prime\:}=-\frac{y}{(x+\frac{2}{y})}
y^'+y=b	y^{\prime\:}+y=b
derivative of sqrt(x)+2	derivative\:\sqrt{x}+2
(d^2)/(dx^2)(((1-2x))/(1+2x))	\frac{d^{2}}{dx^{2}}(\frac{(1-2x)}{1+2x})
derivative of 2-sqrt(x)	\frac{d}{dx}(2-\sqrt{x})
integral of 2/(x^3-x)	\int\:\frac{2}{x^{3}-x}dx
inverse oflaplace s/((s^2+16)(s^2+9))	inverselaplace\:\frac{s}{(s^{2}+16)(s^{2}+9)}
y^{''}-4y^'-5y=0,y(0)=3,y^'(0)=4	y^{\prime\:\prime\:}-4y^{\prime\:}-5y=0,y(0)=3,y^{\prime\:}(0)=4
derivative of x-ln(8x)	\frac{d}{dx}(x-\ln(8x))
derivative of (7x+4)^2	derivative\:(7x+4)^{2}
(dy)/(dx)=3xy	\frac{dy}{dx}=3xy
integral of (x+2x^2)/(sqrt(x))	\int\:\frac{x+2x^{2}}{\sqrt{x}}dx
derivative of x^2arctan(7x)	\frac{d}{dx}(x^{2}\arctan(7x))
integral of (6x-1)/(x^3+4x)	\int\:\frac{6x-1}{x^{3}+4x}dx
integral of 5x^3e^x	\int\:5x^{3}e^{x}dx
derivative of y=ln(sqrt(x+1))	derivative\:y=\ln(\sqrt{x+1})
derivative of 2e^{-2x}	\frac{d}{dx}(2e^{-2x})
derivative of cos^{-2}(x)	\frac{d}{dx}(\cos^{-2}(x))
derivative of (3x^2+7x^4)	\frac{d}{dx}((3x^{2}+7x)^{4})
tangent of f(x)=x^3-9x,\at x=3	tangent\:f(x)=x^{3}-9x,\at\:x=3
integral of (1+1/x)^2 1/(x^2)	\int\:(1+\frac{1}{x})^{2}\frac{1}{x^{2}}dx
derivative of arccos(3x+1)	\frac{d}{dx}(\arccos(3x+1))
integral of 3^xx	\int\:3^{x}xdx
derivative of f(0)= x/(x^2+4)	derivative\:f(0)=\frac{x}{x^{2}+4}
integral from 0 to 1 of ((x^3+1)/(x+1))	\int\:_{0}^{1}(\frac{x^{3}+1}{x+1})dx
(\partial)/(\partial x)(x^{1/2}+y^{1/2})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}+y^{\frac{1}{2}})
area 20+x-x^2,x^2-5x,[4,8]	area\:20+x-x^{2},x^{2}-5x,[4,8]
derivative of e^{cos^2(pit-11)}	derivative\:e^{\cos^{2}(πt-11)}
(\partial)/(\partial x)(5x^2y)	\frac{\partial\:}{\partial\:x}(5x^{2}y)
derivative of xcos(pix)	\frac{d}{dx}(x\cos(πx))
integral from-5 to 5 of 1/(x^{2/3)}	\int\:_{-5}^{5}\frac{1}{x^{\frac{2}{3}}}dx
simplify-arcsin(1/4 x)+x/(sqrt(16-x^2))+C	simplify\:-\arcsin(\frac{1}{4}x)+\frac{x}{\sqrt{16-x^{2}}}+C
integral of (x+1)sqrt(x^2+2x+2)	\int\:(x+1)\sqrt{x^{2}+2x+2}dx
integral of 1/(x^2)sin^2(1/x)	\int\:\frac{1}{x^{2}}\sin^{2}(\frac{1}{x})dx
integral from-2 to 4 of x-9	\int\:_{-2}^{4}x-9dx
derivative of f(x)=6(x-2)	derivative\:f(x)=6(x-2)
derivative of (cos(x+2sec(x))/(8sin(x)))	\frac{d}{dx}(\frac{\cos(x)+2\sec(x)}{8\sin(x)})
integral from-infinity to 3 of 1/(x^2+1)	\int\:_{-\infty\:}^{3}\frac{1}{x^{2}+1}dx
tangent of f(x)=x^3-12x,\at x=1	tangent\:f(x)=x^{3}-12x,\at\:x=1
derivative of (x-13/(sqrt(x)-\sqrt{13)})	\frac{d}{dx}(\frac{x-13}{\sqrt{x}-\sqrt{13}})
slope of (1.2)(-2.14)	slope\:(1.2)(-2.14)
derivative of (sinh(x)/(cosh(x)))	\frac{d}{dx}(\frac{\sinh(x)}{\cosh(x)})
derivative of (x-10/(sqrt(x)-\sqrt{10)})	\frac{d}{dx}(\frac{x-10}{\sqrt{x}-\sqrt{10}})
limit as x approaches infinity of 2+3/x	\lim\:_{x\to\:\infty\:}(2+\frac{3}{x})
integral of 12x^2sqrt(1-x^2)	\int\:12x^{2}\sqrt{1-x^{2}}dx
integral of (x+5)/(sqrt(9-(x-3)^2))	\int\:\frac{x+5}{\sqrt{9-(x-3)^{2}}}dx
integral from-1 to 2 of (5y)/(y^2-y-6)	\int\:_{-1}^{2}\frac{5y}{y^{2}-y-6}dy
derivative of f(x)=x^3-6x^2+9x+5	derivative\:f(x)=x^{3}-6x^{2}+9x+5
tangent of f(x)=x^2-3x+6,\at x=2	tangent\:f(x)=x^{2}-3x+6,\at\:x=2
area 7x^2,x^2+4	area\:7x^{2},x^{2}+4
limit as x approaches infinity of x-x	\lim\:_{x\to\:\infty\:}(x-x)
integral from 0 to 1 of x^3(2x^4+1)^2	\int\:_{0}^{1}x^{3}(2x^{4}+1)^{2}dx
integral of (cos^2(sqrt(x)))/(sqrt(x))	\int\:\frac{\cos^{2}(\sqrt{x})}{\sqrt{x}}dx
(d^3)/(dx^3)(2/x)	\frac{d^{3}}{dx^{3}}(\frac{2}{x})
integral from 1 to 2 of 4/(x^3+x)	\int\:_{1}^{2}\frac{4}{x^{3}+x}dx
limit as x approaches 0 of (1+3x)^{1/x}	\lim\:_{x\to\:0}((1+3x)^{\frac{1}{x}})
(\partial)/(\partial x)(x^2+2y^2+3z^2-9)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}+3z^{2}-9)
integral from 2 to 6 of ln(x)	\int\:_{2}^{6}\ln(x)dx
limit as x approaches-3 of (x^2-9)/(x+3)	\lim\:_{x\to\:-3}(\frac{x^{2}-9}{x+3})
tangent of f(x)=sin(sin(x)),\at x=(4pi)	tangent\:f(x)=\sin(\sin(x)),\at\:x=(4π)
integral of cos(2x)+1	\int\:\cos(2x)+1dx
derivative of \sqrt[4]{(1/(x^3))}	derivative\:\sqrt[4]{(\frac{1}{x^{3}})}

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