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Popular Calculus Problems

derivative of sqrt(2+cos(2x))	\frac{d}{dx}(\sqrt{2+\cos(2x)})
partialfraction x/(x^2-9)	partialfraction\:\frac{x}{x^{2}-9}
d/(dy)(sinh(y))	\frac{d}{dy}(\sinh(y))
implicit x^2+11xy+y^2=11	implicit\:x^{2}+11xy+y^{2}=11
x(x^3+1)y^'+(2x^3-1)y=((x^3-2))/x	x(x^{3}+1)y^{\prime\:}+(2x^{3}-1)y=\frac{(x^{3}-2)}{x}
derivative of 3log_{10}(x)	\frac{d}{dx}(3\log_{10}(x))
(\partial)/(\partial x)(1/(2x+4y^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{2x+4y^{2}})
integral from 0 to 3 of x^2sqrt(9-x^2)	\int\:_{0}^{3}x^{2}\sqrt{9-x^{2}}dx
sum from n=0 to infinity of ((nx)/6)^n	\sum\:_{n=0}^{\infty\:}(\frac{nx}{6})^{n}
limit as x approaches+2 of sqrt(2-x)	\lim\:_{x\to\:+2}(\sqrt{2-x})
derivative of f(x)=(2t-1)(3t-4)^{-1}	derivative\:f(x)=(2t-1)(3t-4)^{-1}
(\partial)/(\partial x)(x^3+2xy+y^2)	\frac{\partial\:}{\partial\:x}(x^{3}+2xy+y^{2})
derivative of 0.015+x	\frac{d}{dx}(0.015+x)
tangent of f(x)=6x^2-10x+4,\at x=1	tangent\:f(x)=6x^{2}-10x+4,\at\:x=1
limit as x approaches 3 of ln(x)	\lim\:_{x\to\:3}(\ln(x))
integral of e^{2y}-ycos(xy)	\int\:e^{2y}-y\cos(xy)dx
derivative of 4.9x^2	\frac{d}{dx}(4.9x^{2})
(\partial}{\partial x}(ln(\frac{x-2)/3))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x-2}{3}))
limit as x approaches 7 of (x-7)/(\|x-7\|)	\lim\:_{x\to\:7}(\frac{x-7}{\left\|x-7\right\|})
limit as x approaches 0 of x^2+3x+1	\lim\:_{x\to\:0}(x^{2}+3x+1)
y^{''}+4y^'+3y=0,y(0)=2,y^'(0)=-1	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=0,y(0)=2,y^{\prime\:}(0)=-1
2sqrt(y)dy= 5/(sqrt(x))dx	2\sqrt{y}dy=\frac{5}{\sqrt{x}}dx
derivative of (sqrt(x)+1/(sqrt(x)+3))	\frac{d}{dx}(\frac{\sqrt{x}+1}{\sqrt{x}+3})
(\partial)/(\partial x)(2/3 y^{-1/3})	\frac{\partial\:}{\partial\:x}(\frac{2}{3}y^{-\frac{1}{3}})
y^'=(x+y-1)^2,y(0)=0	y^{\prime\:}=(x+y-1)^{2},y(0)=0
derivative of (4(-x^2-4)/((x^2-4)^2))	\frac{d}{dx}(\frac{4(-x^{2}-4)}{(x^{2}-4)^{2}})
(x^2sin(x^2))^'	(x^{2}\sin(x^{2}))^{\prime\:}
integral of ((4x^3-6x^4))/(2x^6)	\int\:\frac{(4x^{3}-6x^{4})}{2x^{6}}dx
tangent of f(x)=2x^4+3x-3,(2,35)	tangent\:f(x)=2x^{4}+3x-3,(2,35)
derivative of 9a^2+8a-56	derivative\:9a^{2}+8a-56
sum from t=0 to infinity of 1/(t^{0.51)}	\sum\:_{t=0}^{\infty\:}\frac{1}{t^{0.51}}
f(x)=(x/(\sqrt[4]{2x+1)})^{1/x}	f(x)=(\frac{x}{\sqrt[4]{2x+1}})^{\frac{1}{x}}
integral of-3x^2-6x+45	\int\:-3x^{2}-6x+45dx
tangent of f(x)= 1/(x^4),\at x=1	tangent\:f(x)=\frac{1}{x^{4}},\at\:x=1
integral from 6 to 8 of (32)/((x-6)^3)	\int\:_{6}^{8}\frac{32}{(x-6)^{3}}dx
y^'+y=e^xy^2	y^{\prime\:}+y=e^{x}y^{2}
integral from 1 to 2 of ((2x+1)(x-2))/x	\int\:_{1}^{2}\frac{(2x+1)(x-2)}{x}dx
derivative of f(x)= x/(x-7)	derivative\:f(x)=\frac{x}{x-7}
y^{''}+3y^'+2y= 1/(7+e^x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\frac{1}{7+e^{x}}
derivative of 1+1/(2x)	\frac{d}{dx}(1+\frac{1}{2x})
derivative of y=(sqrt(x)-5)/(sqrt(x)+5)	derivative\:y=\frac{\sqrt{x}-5}{\sqrt{x}+5}
derivative of (2x+1^2sqrt(3(2x+1)+10))	\frac{d}{dx}((2x+1)^{2}\sqrt{3(2x+1)+10})
inverse oflaplace 1/(s^2-s+1)	inverselaplace\:\frac{1}{s^{2}-s+1}
sum from n=0 to infinity of 7(2/3)^n	\sum\:_{n=0}^{\infty\:}7(\frac{2}{3})^{n}
integral of (x^3+1)^2x	\int\:(x^{3}+1)^{2}xdx
limit as x approaches 3 of (x+3)/(x+2)	\lim\:_{x\to\:3}(\frac{x+3}{x+2})
derivative of 7/(8x^5)	\frac{d}{dx}(\frac{7}{8x^{5}})
(\partial)/(\partial y)(ycos(z))	\frac{\partial\:}{\partial\:y}(y\cos(z))
(\partial)/(\partial y)(z^2)	\frac{\partial\:}{\partial\:y}(z^{2})
(\partial)/(\partial x)(xy-x+y)	\frac{\partial\:}{\partial\:x}(xy-x+y)
area 0,x^2,-x+5	area\:0,x^{2},-x+5
integral of 1/(cos(x-1))	\int\:\frac{1}{\cos(x-1)}dx
derivative of f(x)=x^3-2x	derivative\:f(x)=x^{3}-2x
area 4x+10,x^2+6x+6,-2,2	area\:4x+10,x^{2}+6x+6,-2,2
(x^2+16)(dy)/(dx)+xy=5x	(x^{2}+16)\frac{dy}{dx}+xy=5x
derivative of log_{8}(5x^3+3x)	derivative\:\log_{8}(5x^{3}+3x)
integral from 0 to 2 of (1+x^2)	\int\:_{0}^{2}(1+x^{2})dx
(\partial)/(\partial x)((x^2)/(16-y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{16-y^{2}})
integral of 1/(tan(5x))	\int\:\frac{1}{\tan(5x)}dx
tangent of f(x)= 1/(2+3x),(1, 1/5)	tangent\:f(x)=\frac{1}{2+3x},(1,\frac{1}{5})
laplacetransform e^{-2t}t	laplacetransform\:e^{-2t}t
taylor e^x,-4	taylor\:e^{x},-4
(\partial)/(\partial y)((2x+3y)^{10})	\frac{\partial\:}{\partial\:y}((2x+3y)^{10})
tangent of y= 2/x ,(4, 1/2)	tangent\:y=\frac{2}{x},(4,\frac{1}{2})
tangent of f(x)=e^{-x}ln(x),(1,0)	tangent\:f(x)=e^{-x}\ln(x),(1,0)
integral of 1/(x(x^2+4)^2)	\int\:\frac{1}{x(x^{2}+4)^{2}}dx
d/(dθ)(2sin(5θ))	\frac{d}{dθ}(2\sin(5θ))
integral from 1 to 10 of x/(x^2-4)	\int\:_{1}^{10}\frac{x}{x^{2}-4}dx
derivative of g(x)=2^{x^2+1x}	derivative\:g(x)=2^{x^{2}+1x}
(\partial)/(\partial x)(x^2tan(4x^4y))	\frac{\partial\:}{\partial\:x}(x^{2}\tan(4x^{4}y))
integral of 1/(x^2sqrt(x^2-64))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-64}}dx
integral of 1/(sqrt(t^2-8t+25))	\int\:\frac{1}{\sqrt{t^{2}-8t+25}}dt
(dy)/(dx)=(2x)/(y^2)	\frac{dy}{dx}=\frac{2x}{y^{2}}
limit as x approaches 2 of 6*a+x	\lim\:_{x\to\:2}(6\cdot\:a+x)
inverse oflaplace ((18))/(s(s^2+6s+18))	inverselaplace\:\frac{(18)}{s(s^{2}+6s+18)}
3xy^'+y=12x	3xy^{\prime\:}+y=12x
(\partial)/(\partial y)(5x^2y^3)	\frac{\partial\:}{\partial\:y}(5x^{2}y^{3})
(\partial)/(\partial x)(cos(2x-3y^2))	\frac{\partial\:}{\partial\:x}(\cos(2x-3y^{2}))
integral of (-8x+162)/(x^2+9)	\int\:\frac{-8x+162}{x^{2}+9}dx
x(dy)/(dx)=x^2+2x-3	x\frac{dy}{dx}=x^{2}+2x-3
integral of e^xe^{e^x}	\int\:e^{x}e^{e^{x}}dx
sum from n=2 to infinity of 1/(n^2+6n+8)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}+6n+8}
taylor-(3x-4)^3,3	taylor\:-(3x-4)^{3},3
integral from-1 to 64 of 1/(x^{1/3)}	\int\:_{-1}^{64}\frac{1}{x^{\frac{1}{3}}}dx
sum from n=1 to infinity of 2/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{2}{3^{n}}
limit as x approaches 2 of 3+2x+x^2	\lim\:_{x\to\:2}(3+2x+x^{2})
limit as x approaches 3 of (\|x-3\|)/(x+3)	\lim\:_{x\to\:3}(\frac{\left\|x-3\right\|}{x+3})
integral of sin(a)x	\int\:\sin(a)xdx
inverse oflaplace 1/(s^2+3s+2)	inverselaplace\:\frac{1}{s^{2}+3s+2}
derivative of f(t)=(t^2)/(sqrt(t^3+1))	derivative\:f(t)=\frac{t^{2}}{\sqrt{t^{3}+1}}
derivative of (y^{3/2})/3-y^{1/2}	derivative\:\frac{y^{\frac{3}{2}}}{3}-y^{\frac{1}{2}}
derivative of e^{2x}-x	\frac{d}{dx}(e^{2x}-x)
(1/(x^4))^'	(\frac{1}{x^{4}})^{\prime\:}
(\partial)/(\partial x)(4-x^4+2x^2-y^2)	\frac{\partial\:}{\partial\:x}(4-x^{4}+2x^{2}-y^{2})
(\partial)/(\partial x)(4x-sqrt(2y^2+z^2))	\frac{\partial\:}{\partial\:x}(4x-\sqrt{2y^{2}+z^{2}})
derivative of 9e^x+4/(\sqrt[3]{x})	\frac{d}{dx}(9e^{x}+\frac{4}{\sqrt[3]{x}})
limit as x approaches 6 of (x-3)/(x-1)	\lim\:_{x\to\:6}(\frac{x-3}{x-1})
(\partial)/(\partial x)(2e^{-2x}+1/3 e^x)	\frac{\partial\:}{\partial\:x}(2e^{-2x}+\frac{1}{3}e^{x})
integral from 0 to pi/6 of tan(2x)	\int\:_{0}^{\frac{π}{6}}\tan(2x)dx
derivative of f(x)=2e^xcos(x)	derivative\:f(x)=2e^{x}\cos(x)

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