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Popular Calculus Problems

limit as x approaches 6 of (\|6-x\|)/(6-x)	\lim\:_{x\to\:6}(\frac{\left\|6-x\right\|}{6-x})
integral from 0 to pi/8 of tan(4x)	\int\:_{0}^{\frac{π}{8}}\tan(4x)dx
integral of arccos(1)	\int\:\arccos(1)dx
derivative of f(x)=(8x)/(x^2+1)	derivative\:f(x)=\frac{8x}{x^{2}+1}
derivative of y=x^2ln(x^2)	derivative\:y=x^{2}\ln(x^{2})
derivative of sqrt(\sqrt{1+\sqrt{x)}+1}	\frac{d}{dx}(\sqrt{\sqrt{1+\sqrt{x}}+1})
derivative of ln(sqrt(x+3))	derivative\:\ln(\sqrt{x+3})
integral of (e^{2/x})/(x^2)	\int\:\frac{e^{\frac{2}{x}}}{x^{2}}dx
y^'+6y=4x^3e^{-6x}	y^{\prime\:}+6y=4x^{3}e^{-6x}
(dy)/(dx)=5+e^{y-5x+1},y(0)=-1	\frac{dy}{dx}=5+e^{y-5x+1},y(0)=-1
limit as x approaches 2+of-1	\lim\:_{x\to\:2+}(-1)
derivative of 8x+sqrt(x^2+7x+3)	\frac{d}{dx}(8x+\sqrt{x^{2}+7x+3})
laplacetransform e^{17t}t^7	laplacetransform\:e^{17t}t^{7}
tangent of f(x)=50sqrt(x)-5x	tangent\:f(x)=50\sqrt{x}-5x
(\partial)/(\partial y)(cos(y)e^x+2/x)	\frac{\partial\:}{\partial\:y}(\cos(y)e^{x}+\frac{2}{x})
derivative of x^2(x^3-1)	derivative\:x^{2}(x^{3}-1)
limit as x approaches 0 of (b-c)/(x^a)	\lim\:_{x\to\:0}(\frac{b-c}{x^{a}})
derivative of sqrt(4+\sqrt{6x)}	derivative\:\sqrt{4+\sqrt{6x}}
derivative of y=4\sqrt[5]{x}	derivative\:y=4\sqrt[5]{x}
derivative of sqrt(9)	derivative\:\sqrt{9}
limit as x approaches 9 of 9x+\|x-9\|	\lim\:_{x\to\:9}(9x+\left\|x-9\right\|)
derivative of 1/(sqrt(e^x))	\frac{d}{dx}(\frac{1}{\sqrt{e^{x}}})
laplacetransform t^3\delta(t-1)	laplacetransform\:t^{3}\delta(t-1)
limit as x approaches 8 of 2x-1	\lim\:_{x\to\:8}(2x-1)
derivative of cos(14x)	\frac{d}{dx}(\cos(14x))
derivative of (ln(x^2)/(e^{2x)})	\frac{d}{dx}(\frac{\ln(x^{2})}{e^{2x}})
sum from n=0 to infinity of 1/(n^2+3n+2)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+3n+2}
limit as x approaches 0 of (e^x+e^{-x})/(e^x-e^{-x)}	\lim\:_{x\to\:0}(\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}})
derivative of sqrt(1-\sqrt{x)}	\frac{d}{dx}(\sqrt{1-\sqrt{x}})
slope of (0,-4),(1,2)	slope\:(0,-4),(1,2)
(1-5y+x)(dy)/(dx)+y=5x-1	(1-5y+x)\frac{dy}{dx}+y=5x-1
y'(t)=10-e^y,y(0)=1	y\prime\:(t)=10-e^{y},y(0)=1
derivative of y=x^3-(x^2)/(16)	derivative\:y=x^{3}-\frac{x^{2}}{16}
integral of 5x+y	\int\:5x+ydy
derivative of-sqrt(2x)	\frac{d}{dx}(-\sqrt{2x})
integral of sqrt(1+3sin^2(x))	\int\:\sqrt{1+3\sin^{2}(x)}dx
integral of (esqrt(x))/(sqrt(x))	\int\:\frac{e\sqrt{x}}{\sqrt{x}}dx
integral of (sec(x))^6	\int\:(\sec(x))^{6}dx
limit as x approaches 0+of (-5+x)/(4+x)	\lim\:_{x\to\:0+}(\frac{-5+x}{4+x})
integral from 0 to 2 of (4ti-t^3j+4t^7k)	\int\:_{0}^{2}(4ti-t^{3}j+4t^{7}k)dt
derivative of y=x^4+2x^2-x	derivative\:y=x^{4}+2x^{2}-x
limit as x approaches 2 of 2x^3	\lim\:_{x\to\:2}(2x^{3})
derivative of-x^{-3}	\frac{d}{dx}(-x^{-3})
integral of-(x+1)/x	\int\:-\frac{x+1}{x}dx
4y^{''}-4y^'-3y=0	4y^{\prime\:\prime\:}-4y^{\prime\:}-3y=0
implicit (dy)/(dx),y^2=2x	implicit\:\frac{dy}{dx},y^{2}=2x
derivative of 10x^3	\frac{d}{dx}(10x^{3})
(\partial)/(\partial x)(10x+4y)	\frac{\partial\:}{\partial\:x}(10x+4y)
derivative of-4/(x^2)	derivative\:-\frac{4}{x^{2}}
integral of 1/(3-7x)	\int\:\frac{1}{3-7x}dx
derivative of f(x)=arcsin(x^6)	derivative\:f(x)=\arcsin(x^{6})
(\partial)/(\partial x)(-x/((x^2+y^2+1)))	\frac{\partial\:}{\partial\:x}(-\frac{x}{(x^{2}+y^{2}+1)})
derivative of sqrt(2+ln(x))	\frac{d}{dx}(\sqrt{2+\ln(x)})
derivative of acos(2x)	\frac{d}{dx}(a\cos(2x))
integral of 8cos(θ)	\int\:8\cos(θ)dθ
integral of tan^4(3x)	\int\:\tan^{4}(3x)dx
(\partial)/(\partial x)(ln(xyz))	\frac{\partial\:}{\partial\:x}(\ln(xyz))
derivative of (2x-5/(x+1))	\frac{d}{dx}(\frac{2x-5}{x+1})
limit as x approaches 0 of 2xcot(4x)	\lim\:_{x\to\:0}(2x\cot(4x))
derivative of y=(6x)/(x+2)	derivative\:y=\frac{6x}{x+2}
laplacetransform e^{-t}	laplacetransform\:e^{-t}
integral of 1/(u^3)	\int\:\frac{1}{u^{3}}du
(\partial)/(\partial x)(x^7+3^y+x^y)	\frac{\partial\:}{\partial\:x}(x^{7}+3^{y}+x^{y})
d/(dy)(-ln(y))	\frac{d}{dy}(-\ln(y))
y^{''}-6y^'+9y=xe^x	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=xe^{x}
slope of (-5,6),(-3,4)	slope\:(-5,6),(-3,4)
integral of (x^2)/((121+x^2)^2)	\int\:\frac{x^{2}}{(121+x^{2})^{2}}dx
integral of (y^3e^{y^2})/((y^2+1)^2)	\int\:\frac{y^{3}e^{y^{2}}}{(y^{2}+1)^{2}}dy
area f(x)=x^2-2x,(0,2)	area\:f(x)=x^{2}-2x,(0,2)
derivative of x-3\sqrt[3]{x}	\frac{d}{dx}(x-3\sqrt[3]{x})
y^{''}-8y^'+15y=4e^t	y^{\prime\:\prime\:}-8y^{\prime\:}+15y=4e^{t}
(\partial)/(\partial x)(2x+3e^y+xy)	\frac{\partial\:}{\partial\:x}(2x+3e^{y}+xy)
inverse oflaplace (10s)/((s+1)(s+6))	inverselaplace\:\frac{10s}{(s+1)(s+6)}
derivative of (4(y-x\frac{dy/(dx))}{y^2})	\frac{d}{dx}(\frac{4(y-x\frac{dy}{dx})}{y^{2}})
integral of (ln^2(x))/(3x)	\int\:\frac{\ln^{2}(x)}{3x}dx
derivative of y=ln(1-x^2)	derivative\:y=\ln(1-x^{2})
(\partial)/(\partial y)(2y^3-6y+x^2)	\frac{\partial\:}{\partial\:y}(2y^{3}-6y+x^{2})
limit as x approaches+0+of 1/x-1/(x^2+x)	\lim\:_{x\to\:+0+}(\frac{1}{x}-\frac{1}{x^{2}+x})
limit as x approaches 0 of x^4sin(4/x)	\lim\:_{x\to\:0}(x^{4}\sin(\frac{4}{x}))
inverse oflaplace (1+4s)/(s(2s^2+2s+1))	inverselaplace\:\frac{1+4s}{s(2s^{2}+2s+1)}
limit as x approaches 1 of sqrt((x^5-1)/(x-1))	\lim\:_{x\to\:1}(\sqrt{\frac{x^{5}-1}{x-1}})
derivative of sin((pix/4))	\frac{d}{dx}(\sin(\frac{πx}{4}))
taylor 1/x ,1	taylor\:\frac{1}{x},1
derivative of 6sin(4x)	derivative\:6\sin(4x)
integral of 3e^{-0.5x}	\int\:3e^{-0.5x}dx
integral of 5e^7	\int\:5e^{7}dx
derivative of ln(x^2+3)	derivative\:\ln(x^{2}+3)
inverse oflaplace (s+4)/((s+1)^2)	inverselaplace\:\frac{s+4}{(s+1)^{2}}
inverse oflaplace ((-2))/((6s+s^2))	inverselaplace\:\frac{(-2)}{(6s+s^{2})}
ydx=2(x+y)dy	ydx=2(x+y)dy
(x+y)dx+(x+2y)dy=0,y(2)=3	(x+y)dx+(x+2y)dy=0,y(2)=3
limit as x approaches 0-of 1/(1+e^{1/x)}	\lim\:_{x\to\:0-}(\frac{1}{1+e^{\frac{1}{x}}})
derivative of 2arctan(4x)	\frac{d}{dx}(2\arctan(4x))
limit as x approaches 0 of x^2ln(x^2)	\lim\:_{x\to\:0}(x^{2}\ln(x^{2}))
integral of 1/((x^2-16)^{3/2)}	\int\:\frac{1}{(x^{2}-16)^{\frac{3}{2}}}dx
integral of x^{3/2}ln(x)	\int\:x^{\frac{3}{2}}\ln(x)dx
integral of 1/(4+4x^2)	\int\:\frac{1}{4+4x^{2}}dx
integral of 1/((x+4)^2(x-3))	\int\:\frac{1}{(x+4)^{2}(x-3)}dx
tangent of f(x)=x^2+7,(1,8)	tangent\:f(x)=x^{2}+7,(1,8)
derivative of ln(arccos(x))	\frac{d}{dx}(\ln(\arccos(x)))

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