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Popular Calculus Problems

(\partial)/(\partial x)(ln(x^2y))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}y))
limit as x approaches 0 of xsin((3pi)/x)	\lim\:_{x\to\:0}(x\sin(\frac{3π}{x}))
derivative of y=-(14)/(x^5)	derivative\:y=-\frac{14}{x^{5}}
(\partial)/(\partial x)(6x^3cos(6x^2y))	\frac{\partial\:}{\partial\:x}(6x^{3}\cos(6x^{2}y))
area y=x^2,y=3	area\:y=x^{2},y=3
integral from 0 to pi/4 of sec^2(x)	\int\:_{0}^{\frac{π}{4}}\sec^{2}(x)dx
d/(ds)(ln(s+(sqrt(s^2+4))/2)sqrt(2))	\frac{d}{ds}(\ln(s+\frac{\sqrt{s^{2}+4}}{2})\sqrt{2})
derivative of 2^{x/3}	\frac{d}{dx}(2^{\frac{x}{3}})
tangent of sqrt(4x+20)	tangent\:\sqrt{4x+20}
tangent of f(x)=(x+3)/(2x+1),\at x=-1	tangent\:f(x)=\frac{x+3}{2x+1},\at\:x=-1
derivative of 2x^{-1/4}	derivative\:2x^{-\frac{1}{4}}
limit as x approaches infinity of 9^x	\lim\:_{x\to\:\infty\:}(9^{x})
derivative of 1/(1+ln(x))	\frac{d}{dx}(\frac{1}{1+\ln(x)})
y^'-y/x =(sqrt(xy))/x	y^{\prime\:}-\frac{y}{x}=\frac{\sqrt{xy}}{x}
(dx}{dt}=x+\frac{t^2)/2 ,x(0)=0	\frac{dx}{dt}=x+\frac{t^{2}}{2},x(0)=0
derivative of 1/(x^{10})	\frac{d}{dx}(\frac{1}{x^{10}})
tangent of f(x)=(5x)/(x-3),\at (4)	tangent\:f(x)=\frac{5x}{x-3},\at\:(4)
integral of (2+sqrt(x)+x)/x	\int\:\frac{2+\sqrt{x}+x}{x}dx
integral from 0 to 1 of xe^{7x}	\int\:_{0}^{1}xe^{7x}dx
tangent of y= 5/(sqrt(x))(1.5)	tangent\:y=\frac{5}{\sqrt{x}}(1.5)
y^{''}+14y^'+65y=0	y^{\prime\:\prime\:}+14y^{\prime\:}+65y=0
tangent of f(x)=sqrt(3x+10),(2,4)	tangent\:f(x)=\sqrt{3x+10},(2,4)
integral of (26)/((x-1)(x^2+25))	\int\:\frac{26}{(x-1)(x^{2}+25)}dx
derivative of (x^2-7x+4)sqrt(25-x^2)	derivative\:(x^{2}-7x+4)\sqrt{25-x^{2}}
integral of (x+1)/3	\int\:\frac{x+1}{3}dx
xy^2dx+(1+x^2y)dy=0	xy^{2}dx+(1+x^{2}y)dy=0
integral of e^{(x^2-ln(x))}	\int\:e^{(x^{2}-\ln(x))}dx
inverse oflaplace ((1))/((s^2+1)^2)	inverselaplace\:\frac{(1)}{(s^{2}+1)^{2}}
integral from-pi/2 to pi of xsin(\|x\|)	\int\:_{-\frac{π}{2}}^{π}x\sin(\left\|x\right\|)dx
derivative of arctan(x-2)	\frac{d}{dx}(\arctan(x-2))
derivative of f(x)=3xsqrt(2-3x)	derivative\:f(x)=3x\sqrt{2-3x}
limit as x approaches infinity of 4cos(x)	\lim\:_{x\to\:\infty\:}(4\cos(x))
derivative of 1+t/(45t^2+30t)	derivative\:1+\frac{t}{45t^{2}+30t}
derivative of 1/6 ln\|3sec(2x-2\|+C)	\frac{d}{dx}(\frac{1}{6}\ln\left\|3\sec(2x)-2\right\|+C)
integral from 0 to infinity of 1/(x+1)	\int\:_{0}^{\infty\:}\frac{1}{x+1}dx
sum from n=0 to infinity}(-2)^{3-2n of 3	\sum\:_{n=0}^{\infty\:}(-2)^{3-2n}3
(\partial)/(\partial x)(2xy+2x)	\frac{\partial\:}{\partial\:x}(2xy+2x)
(dy)/(dx)=y-x,y(0)= 2/3	\frac{dy}{dx}=y-x,y(0)=\frac{2}{3}
x^'=(x^2-1)t	x^{\prime\:}=(x^{2}-1)t
inverse oflaplace-2e^{-ln(2)s}	inverselaplace\:-2\cdot\:e^{-\ln(2)\cdot\:s}
(\partial)/(\partial y)(4xy)	\frac{\partial\:}{\partial\:y}(4xy)
derivative of 1/(3+x^2)	\frac{d}{dx}(\frac{1}{3+x^{2}})
integral of 1/(sqrt(x+1)+x-1)	\int\:\frac{1}{\sqrt{x+1}+x-1}dx
integral of 4/((4+x^2)^2)	\int\:\frac{4}{(4+x^{2})^{2}}dx
tangent of f(x)=x^2+7,(-4,23)	tangent\:f(x)=x^{2}+7,(-4,23)
limit as x approaches 1+of x^{4/(1-x)}	\lim\:_{x\to\:1+}(x^{\frac{4}{1-x}})
integral of (-2x-6)/(x^3-2x^2-3x)	\int\:\frac{-2x-6}{x^{3}-2x^{2}-3x}dx
limit as x approaches 1+of 4/(x-1)	\lim\:_{x\to\:1+}(\frac{4}{x-1})
(\partial)/(\partial x)(2x^2y-2x+4y^3)	\frac{\partial\:}{\partial\:x}(2x^{2}y-2x+4y^{3})
limit as x approaches 0 of x^{2sqrt(x)}	\lim\:_{x\to\:0}(x^{2\sqrt{x}})
d/(dv)(vi)	\frac{d}{dv}(vi)
sum from n=1 to infinity of 2(0.1)^n	\sum\:_{n=1}^{\infty\:}2(0.1)^{n}
derivative of 1/({f(x)x^'({f}(x)(x)^{-1}(x))})	\frac{d}{dx}(\frac{1}{{f}(x)x^{\prime\:}({f}(x)(x)^{-1}(x))})
derivative of (cos(x)/2)	\frac{d}{dx}(\frac{\cos(x)}{2})
y^{''}-4y^'+4y=e^{2t}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=e^{2t}
limit as x approaches 4 of x/(x^2-16)	\lim\:_{x\to\:4}(\frac{x}{x^{2}-16})
limit as x approaches 1 of (x^2-3)/(x-6)	\lim\:_{x\to\:1}(\frac{x^{2}-3}{x-6})
integral of sin((pix)/L)	\int\:\sin(\frac{πx}{L})dx
derivative of 1/3 x^2	\frac{d}{dx}(\frac{1}{3}x^{2})
y^3-(6x+6)+3xy^2(dy)/(dx)=0	y^{3}-(6x+6)+3xy^{2}\frac{dy}{dx}=0
integral of (e^{2x})/(e^{2x)+2}	\int\:\frac{e^{2x}}{e^{2x}+2}dx
derivative of ln(1/(x-y))	\frac{d}{dx}(\ln(\frac{1}{x-y}))
integral of (2x+11)/(x^2+x-6)	\int\:\frac{2x+11}{x^{2}+x-6}dx
integral of 1/(x^2)cos(1/x)	\int\:\frac{1}{x^{2}}\cos(\frac{1}{x})dx
derivative of (x^2/(x^2-2))	\frac{d}{dx}(\frac{x^{2}}{x^{2}-2})
(\partial)/(\partial x)((6-x-y)^2)	\frac{\partial\:}{\partial\:x}((6-x-y)^{2})
(dy)/(dt)=-2(y-3)	\frac{dy}{dt}=-2(y-3)
(\partial)/(\partial x)(17xye^{-x^2-y^2})	\frac{\partial\:}{\partial\:x}(17xye^{-x^{2}-y^{2}})
(\partial)/(\partial x)(c(1+m*x)-c(1+m)^x)	\frac{\partial\:}{\partial\:x}(c(1+m\cdot\:x)-c(1+m)^{x})
sum from n=1 to infinity of n/(3n^3+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{3n^{3}+1}
derivative of \| x/2 \|	\frac{d}{dx}(\left\|\frac{x}{2}\right\|)
y^{''}-y^'+1/4 y=0	y^{\prime\:\prime\:}-y^{\prime\:}+\frac{1}{4}y=0
limit as x approaches-1+of (3x-5)/(x+1)	\lim\:_{x\to\:-1+}(\frac{3x-5}{x+1})
tangent of-3/(sqrt(x))	tangent\:-\frac{3}{\sqrt{x}}
solvefor x,(d^2y)/(dx^2)=y^2	solvefor\:x,\frac{d^{2}y}{dx^{2}}=y^{2}
(arctan(cos(x)))^'	(\arctan(\cos(x)))^{\prime\:}
y^{''}-y^'-6y=20e^{-2x}	y^{\prime\:\prime\:}-y^{\prime\:}-6y=20e^{-2x}
(\partial)/(\partial x)(8xy^5+x^8y^2)	\frac{\partial\:}{\partial\:x}(8xy^{5}+x^{8}y^{2})
2y^{'''}+3y^{''}-8y^'+3y=0	2y^{\prime\:\prime\:\prime\:}+3y^{\prime\:\prime\:}-8y^{\prime\:}+3y=0
derivative of (x^2)/4	derivative\:\frac{x^{2}}{4}
integral from 4 to 6 of 2pi(y)(4/y)	\int\:_{4}^{6}2π(y)(\frac{4}{y})dy
derivative of sqrt(x^2+1)-x	\frac{d}{dx}(\sqrt{x^{2}+1}-x)
integral of 1/24 x	\int\:\frac{1}{24}xdx
limit as x approaches 3 of x+2	\lim\:_{x\to\:3}(x+2)
tangent of f(x)=x^2+4x	tangent\:f(x)=x^{2}+4x
derivative of-(49/((1+7x)^2))	\frac{d}{dx}(-\frac{49}{(1+7x)^{2}})
integral of (x^2)/(x^4-2x^2-8)	\int\:\frac{x^{2}}{x^{4}-2x^{2}-8}dx
(\partial)/(\partial x)(pix^2y)	\frac{\partial\:}{\partial\:x}(πx^{2}y)
limit as n approaches infinity of 1/6	\lim\:_{n\to\:\infty\:}(\frac{1}{6})
integral of (3cos(3x)-5sin(5x))	\int\:(3\cos(3x)-5\sin(5x))dx
f(x)=sqrt(3-x)	f(x)=\sqrt{3-x}
integral from 9 to 1 of (-15sqrt(x))	\int\:_{9}^{1}(-15\sqrt{x})dx
limit as t approaches 0 of (t^3-1)/(t-1)	\lim\:_{t\to\:0}(\frac{t^{3}-1}{t-1})
derivative of 6/((x-3^4))	\frac{d}{dx}(\frac{6}{(x-3)^{4}})
integral of 7x*(e^{3x})/7	\int\:7x\cdot\:\frac{e^{3x}}{7}dx
limit as x approaches 0+of x+2	\lim\:_{x\to\:0+}(x+2)
laplacetransform 3-sin(2t)+e^{5t}	laplacetransform\:3-\sin(2t)+e^{5t}
derivative of 38(2e^{x^2}x^2+e^{x^2})	derivative\:38(2e^{x^{2}}x^{2}+e^{x^{2}})
(dy)/(dx)=sin(x^2)	\frac{dy}{dx}=\sin(x^{2})
derivative of (2+1e^{2x})	\frac{d}{dx}((2+1)e^{2x})

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