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Popular Calculus Problems

derivative of (3x+1(5x-4))	\frac{d}{dx}((3x+1)(5x-4))
(\partial)/(\partial x)(cos(zw))	\frac{\partial\:}{\partial\:x}(\cos(zw))
sum from n=1 to infinity of (n!)/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{10^{n}}
derivative of (x^4-5x^3+sqrt(x))/(x^2)	derivative\:\frac{x^{4}-5x^{3}+\sqrt{x}}{x^{2}}
integral of (12)/(r^2+1)	\int\:\frac{12}{r^{2}+1}dr
integral of 1/(sqrt(100+x^2))	\int\:\frac{1}{\sqrt{100+x^{2}}}dx
derivative of (x+1(x-1)^2)	\frac{d}{dx}((x+1)(x-1)^{2})
integral of (e^{2x})/((1+e^{2x))^2}	\int\:\frac{e^{2x}}{(1+e^{2x})^{2}}dx
taylor 1/x	taylor\:\frac{1}{x}
(\partial)/(\partial x)(5y^2-xy+y^3sin(y))	\frac{\partial\:}{\partial\:x}(5y^{2}-xy+y^{3}\sin(y))
integral of (4sqrt(x)-1/(2sqrt(x)))	\int\:(4\sqrt{x}-\frac{1}{2\sqrt{x}})dx
integral of 1/(y^2-16)	\int\:\frac{1}{y^{2}-16}dy
y^'=t^{1/4}-y	y^{\prime\:}=t^{\frac{1}{4}}-y
integral from-7 to 7 of (49-x^2)	\int\:_{-7}^{7}(49-x^{2})dx
derivative of ln((sqrt(x+3)/(e^{3x)}))	\frac{d}{dx}(\ln(\frac{\sqrt{x+3}}{e^{3x}}))
(\partial)/(\partial x)(x/(9+y))	\frac{\partial\:}{\partial\:x}(\frac{x}{9+y})
integral of 1/((x^2-361)^{3/2)}	\int\:\frac{1}{(x^{2}-361)^{\frac{3}{2}}}dx
derivative of y=sqrt(7x^3-6x^2-8/x)	derivative\:y=\sqrt{7x^{3}-6x^{2}-\frac{8}{x}}
4y^{''}-y^'+y=0	4y^{\prime\:\prime\:}-y^{\prime\:}+y=0
y^{''}+2y^'-y=10	y^{\prime\:\prime\:}+2y^{\prime\:}-y=10
(dy)/(dx)=sqrt(1-9y^2),y(-1)=0	\frac{dy}{dx}=\sqrt{1-9y^{2}},y(-1)=0
limit as x approaches 0 of (\|sin(x)\|)/x	\lim\:_{x\to\:0}(\frac{\left\|\sin(x)\right\|}{x})
derivative of-(600/(x^2)+4)	\frac{d}{dx}(-\frac{600}{x^{2}}+4)
tangent of f(x)=4x-3x^2,\at x=2	tangent\:f(x)=4x-3x^{2},\at\:x=2
derivative of e^{,\at}sin(bt)	derivative\:e^{,\at\:}\sin(bt)
integral of csc(x)(csc(x)-cot(x))	\int\:\csc(x)(\csc(x)-\cot(x))dx
inverse oflaplace 1/(s^2+5s)	inverselaplace\:\frac{1}{s^{2}+5s}
tangent of y=x^3-2x^2+5,(2,5)	tangent\:y=x^{3}-2x^{2}+5,(2,5)
x^2y^'+2xy=ln(x),y(1)=8	x^{2}y^{\prime\:}+2xy=\ln(x),y(1)=8
integral of x/((x+1)^2)	\int\:\frac{x}{(x+1)^{2}}dx
integral of (x+3)/(sqrt(x^2+4))	\int\:\frac{x+3}{\sqrt{x^{2}+4}}dx
integral of 1/(3sin(x)+4cos(x))	\int\:\frac{1}{3\sin(x)+4\cos(x)}dx
derivative of (5x^3+4^2)	\frac{d}{dx}((5x^{3}+4)^{2})
integral of (arctan(x))/(1+x^2)	\int\:\frac{\arctan(x)}{1+x^{2}}dx
7t*(dy)/(dt)+3y=sqrt(t)	7t\cdot\:\frac{dy}{dt}+3y=\sqrt{t}
integral of (2e^{2x})/(e^{2x)+14e^x+48}	\int\:\frac{2e^{2x}}{e^{2x}+14e^{x}+48}dx
integral of t^3sqrt(9t^4+1)	\int\:t^{3}\sqrt{9t^{4}+1}dt
(dy)/(dx)=3x^2(1+y^2)	\frac{dy}{dx}=3x^{2}(1+y^{2})
y^'=(4xsec(y/x)+y)/x	y^{\prime\:}=\frac{4x\sec(\frac{y}{x})+y}{x}
y^{''}+piy=0	y^{\prime\:\prime\:}+πy=0
integral of (cos^2(t))	\int\:(\cos^{2}(t))dt
sum from n=2 to infinity of sin(1/n)	\sum\:_{n=2}^{\infty\:}\sin(\frac{1}{n})
integral from-pi to pi of x^2cos(2x)	\int\:_{-π}^{π}x^{2}\cos(2x)dx
integral of sin^2(7x)cos^2(7x)	\int\:\sin^{2}(7x)\cos^{2}(7x)dx
derivative of 6(5)^2-2(5)+9	derivative\:6(5)^{2}-2(5)+9
derivative of e^{2x}+x^2-16	\frac{d}{dx}(e^{2x}+x^{2}-16)
integral from 0 to 2 of sqrt((1+3x^2))	\int\:_{0}^{2}\sqrt{(1+3x^{2})}dx
inverse oflaplace (s^2+8)/((s+2)^4)	inverselaplace\:\frac{s^{2}+8}{(s+2)^{4}}
sum from n=-4 to infinity of (-4/11)^n	\sum\:_{n=-4}^{\infty\:}(-\frac{4}{11})^{n}
(\partial)/(\partial z)(x+z)	\frac{\partial\:}{\partial\:z}(x+z)
inverse oflaplace 2/(s*(s+2))	inverselaplace\:\frac{2}{s\cdot\:(s+2)}
integral from 2 to 7 of t^4ln(2t)	\int\:_{2}^{7}t^{4}\ln(2t)dt
derivative of ln(ln(4x))	\frac{d}{dx}(\ln(\ln(4x)))
derivative of (x^2-4x)/(x+1)	derivative\:\frac{x^{2}-4x}{x+1}
y^{''}+2y^'=sin(x)	y^{\prime\:\prime\:}+2y^{\prime\:}=\sin(x)
derivative of sec^2(3x*3)	\frac{d}{dx}(\sec^{2}(3x)\cdot\:3)
limit as x approaches-10-of sqrt(4x+40)	\lim\:_{x\to\:-10-}(\sqrt{4x+40})
tangent of f(x)=26-x^2,(-5,1)	tangent\:f(x)=26-x^{2},(-5,1)
derivative of f(x)=2xe^{-x}	derivative\:f(x)=2xe^{-x}
integral of 1/(sqrt(2x+1))	\int\:\frac{1}{\sqrt{2x+1}}dx
maclaurin f(x)= 1/(2x-5)	maclaurin\:f(x)=\frac{1}{2x-5}
derivative of 2sqrt(x^2)	\frac{d}{dx}(2\sqrt{x^{2}})
derivative of 3x+5	derivative\:3x+5
(dy)/(dt)=4y(1-y)	\frac{dy}{dt}=4y(1-y)
integral from 1 to 2 of 2/(x^3+x)	\int\:_{1}^{2}\frac{2}{x^{3}+x}dx
derivative of \sqrt[4]{x^5+6x}	derivative\:\sqrt[4]{x^{5}+6x}
laplacetransform e^{3t}	laplacetransform\:e^{3t}
limit as x approaches 2 of xsqrt(4-x^2)	\lim\:_{x\to\:2}(x\sqrt{4-x^{2}})
integral of x^2+1/((3x)^2)	\int\:x^{2}+\frac{1}{(3x)^{2}}dx
derivative of 2x^3-15x^2+36x+5	\frac{d}{dx}(2x^{3}-15x^{2}+36x+5)
area x^2-x,3x+5	area\:x^{2}-x,3x+5
derivative of ((x-2^2)/4)	\frac{d}{dx}(\frac{(x-2)^{2}}{4})
2x^3y^'=y(y^2+3x^2)	2x^{3}y^{\prime\:}=y(y^{2}+3x^{2})
integral of 6x+1	\int\:6x+1dx
tangent of y=-(x^2)/(40),(-4sqrt(5),-2)	tangent\:y=-\frac{x^{2}}{40},(-4\sqrt{5},-2)
derivative of f(x(2x^2-4))	\frac{d}{dx}(f(x)(2x^{2}-4))
area 4x,x^3	area\:4x,x^{3}
(\partial)/(\partial x)((x+1)^2)	\frac{\partial\:}{\partial\:x}((x+1)^{2})
factor 5+5t^2-t-t^3	factor\:5+5t^{2}-t-t^{3}
limit as y approaches-1 of (y+1)/(y^3+1)	\lim\:_{y\to\:-1}(\frac{y+1}{y^{3}+1})
inverse oflaplace 1/x*(25)/(x^2+25)	inverselaplace\:\frac{1}{x}\cdot\:\frac{25}{x^{2}+25}
derivative of 3/2 sec(x)	\frac{d}{dx}(\frac{3}{2}\sec(x))
integral of e+sec^2(x)-e^x	\int\:e+\sec^{2}(x)-e^{x}dx
derivative of f(x)=x^3+2	derivative\:f(x)=x^{3}+2
(dy)/(dx)=xy^3(1+x^2)^{-1/2}	\frac{dy}{dx}=xy^{3}(1+x^{2})^{-\frac{1}{2}}
derivative of x^3-y^3	\frac{d}{dx}(x^{3}-y^{3})
derivative of 2/(9x^{5/3})	\frac{d}{dx}(\frac{2}{9x^{\frac{5}{3}}})
area y^2=x+6,y^2=2-x	area\:y^{2}=x+6,y^{2}=2-x
derivative of 4cos(3x)	\frac{d}{dx}(4\cos(3x))
integral from 1 to 2 of tan(xy)	\int\:_{1}^{2}\tan(xy)dy
derivative of 8x^4+5x^3-x^2+4x-1	\frac{d}{dx}(8x^{4}+5x^{3}-x^{2}+4x-1)
laplacetransform-7(t-4)	laplacetransform\:-7(t-4)
derivative of x(2x+1^5)	\frac{d}{dx}(x(2x+1)^{5})
(dy)/(dx)=5y+y^2	\frac{dy}{dx}=5y+y^{2}
tangent of f(x)=sin(x)+1/2 e^x	tangent\:f(x)=\sin(x)+\frac{1}{2}e^{x}
integral of sin(3θ)cos(2θ)	\int\:\sin(3θ)\cos(2θ)dθ
(dy)/(dx)=(3sec(y))/((x+5)^2)	\frac{dy}{dx}=\frac{3\sec(y)}{(x+5)^{2}}
derivative of f(u)= u/(u+a/u)	derivative\:f(u)=\frac{u}{u+\frac{a}{u}}
y^'=-x(y+1),y(0)=2	y^{\prime\:}=-x(y+1),y(0)=2
(\partial)/(\partial y)(2x+sqrt(y))	\frac{\partial\:}{\partial\:y}(2x+\sqrt{y})

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