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Popular Calculus Problems

x^2y^{''}-2xy^'+2y=4x^2	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}+2y=4x^{2}
derivative of csc^7(2t^pi+pi^3)	derivative\:\csc^{7}(2t^{π}+π^{3})
limit as x approaches 6-of f(x)	\lim\:_{x\to\:6-}(f(x))
integral of sqrt(x)*x	\int\:\sqrt{x}\cdot\:xdx
integral of 1/(e^{x/a)-e^{-x/a}}	\int\:\frac{1}{e^{\frac{x}{a}}-e^{-\frac{x}{a}}}dx
derivative of-tan(x)	derivative\:-\tan(x)
inverse oflaplace 1/((s^2-6s+10))	inverselaplace\:\frac{1}{(s^{2}-6s+10)}
(\partial ^2)/(\partial x^2)(e^{3x+4y}cos(5z))	\frac{\partial\:^{2}}{\partial\:x^{2}}(e^{3x+4y}\cos(5z))
inverse oflaplace 2/(5(s+3)^2+125)	inverselaplace\:\frac{2}{5(s+3)^{2}+125}
derivative of (x^2/(sqrt(x^3+1)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x^{3}+1}})
f(x)=4sin(4x)	f(x)=4\sin(4x)
derivative of ln(3+x^2)	\frac{d}{dx}(\ln(3+x^{2}))
x^'+6x=0	x^{\prime\:}+6x=0
sum from n=0 to infinity of 3*(-2/5)^n	\sum\:_{n=0}^{\infty\:}3\cdot\:(-\frac{2}{5})^{n}
integral of (x^2+1)e^{2x}	\int\:(x^{2}+1)e^{2x}dx
derivative of f(x)=5e^x	derivative\:f(x)=5e^{x}
derivative of 3/4 x^{3/2}	\frac{d}{dx}(\frac{3}{4}x^{\frac{3}{2}})
limit as x approaches 2 of 3x^2+7x-1	\lim\:_{x\to\:2}(3x^{2}+7x-1)
derivative of tan(t)-e^{-t}	derivative\:\tan(t)-e^{-t}
integral of (cos(x))/(sin^3(x)-4sin(x))	\int\:\frac{\cos(x)}{\sin^{3}(x)-4\sin(x)}dx
integral of (csc^2(θ)+9)	\int\:(\csc^{2}(θ)+9)dθ
area f(x)=cos(x),0, pi/4	area\:f(x)=\cos(x),0,\frac{π}{4}
tangent of f(x)=(x^3)/2-4/(3x),\at x=2	tangent\:f(x)=\frac{x^{3}}{2}-\frac{4}{3x},\at\:x=2
y=e^{mx}m	y=e^{mx}m
derivative of 3x^2-3x	\frac{d}{dx}(3x^{2}-3x)
(y^3-xy^2)dx+2x^2ydy=0	(y^{3}-xy^{2})dx+2x^{2}ydy=0
limit as x approaches 4 of 6-3x	\lim\:_{x\to\:4}(6-3x)
derivative of ccos(t+t^2,t)	\frac{d}{dx}(c\cos(t)+t^{2},t)
derivative of arcsec(e^{3x})	\frac{d}{dx}(\arcsec(e^{3x}))
tangent of f(x)=-3+(x+4)^2,\at x=-5	tangent\:f(x)=-3+(x+4)^{2},\at\:x=-5
derivative of e^{(x^2/(2a)})	\frac{d}{dx}(e^{\frac{x^{2}}{2a}})
derivative of sin(2xdx)	\frac{d}{dx}(\sin(2x)dx)
(xysin(x)+2ycos(x))dx+(2xcos(x))dy=0	(xy\sin(x)+2y\cos(x))dx+(2x\cos(x))dy=0
limit as h approaches 0 of ((2-h)^3-8)/h	\lim\:_{h\to\:0}(\frac{(2-h)^{3}-8}{h})
integral of sin(y^3)	\int\:\sin(y^{3})dy
(\partial)/(\partial x)(sin(pi(3x-5y)))	\frac{\partial\:}{\partial\:x}(\sin(π(3x-5y)))
taylor 1/(1+1/5 x^3)	taylor\:\frac{1}{1+\frac{1}{5}x^{3}}
(\partial)/(\partial x)((xy-2)e^{-xy})	\frac{\partial\:}{\partial\:x}((xy-2)e^{-xy})
derivative of (((2x+5)^7))/(14)	derivative\:\frac{((2x+5)^{7})}{14}
derivative of 0.8*x^4	\frac{d}{dx}(0.8\cdot\:x^{4})
integral of xsin^2(x)cos^3(x)	\int\:x\sin^{2}(x)\cos^{3}(x)dx
limit as x approaches 125 of (x-125)/(\sqrt[3]{x)-5}	\lim\:_{x\to\:125}(\frac{x-125}{\sqrt[3]{x}-5})
integral of (4x^2+8x+5)^6(x+1)	\int\:(4x^{2}+8x+5)^{6}(x+1)dx
integral of 1/((x+7)(x^2+16))	\int\:\frac{1}{(x+7)(x^{2}+16)}dx
integral of (2x^3+x+1)/(x^2+9)	\int\:\frac{2x^{3}+x+1}{x^{2}+9}dx
derivative of sqrt(1-9x)	derivative\:\sqrt{1-9x}
integral from 0 to 4 of 0.125x^3	\int\:_{0}^{4}0.125x^{3}dx
integral of 1/2 e^{x^2}	\int\:\frac{1}{2}e^{x^{2}}dx
integral of 12xy	\int\:12xydx
derivative of (2y/x)	\frac{d}{dx}(\frac{2y}{x})
integral of 9sin^4(x)cos^2(x)	\int\:9\sin^{4}(x)\cos^{2}(x)dx
derivative of y=x^2e^{-3x}	derivative\:y=x^{2}e^{-3x}
integral of s/(sqrt(3s^2+1))	\int\:\frac{s}{\sqrt{3s^{2}+1}}ds
dx=xsqrt(x^2-16dy)	dx=x\sqrt{x^{2}-16dy}
derivative of a{r}(xcos(x))	\frac{d}{dx}(a{r}(x)\cos(x))
integral from 0 to 5 of x	\int\:_{0}^{5}xdx
integral of 1/(x^2sqrt(10x+1))	\int\:\frac{1}{x^{2}\sqrt{10x+1}}dx
integral of e^θsin(θ)	\int\:e^{θ}\sin(θ)dθ
sum from n=1 to infinity}(((-3)^{n-1 of))/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{((-3)^{n-1})}{5^{n}}
integral of 2sin^3(x)	\int\:2\sin^{3}(x)dx
limit as x approaches infinity of xa	\lim\:_{x\to\:\infty\:}(xa)
derivative of (x^3-6/(x^2))	\frac{d}{dx}(\frac{x^{3}-6}{x^{2}})
integral of 1/(x^{1/2)+x^{1/3}}	\int\:\frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}dx
derivative of arctan(sin(ln(x^3)))	\frac{d}{dx}(\arctan(\sin(\ln(x^{3}))))
integral of ((2x^2-x+3))/(sqrt(x))	\int\:\frac{(2x^{2}-x+3)}{\sqrt{x}}dx
slope of y=2x^3-x^2+3	slope\:y=2x^{3}-x^{2}+3
(dy)/(dx)=4xy	\frac{dy}{dx}=4xy
integral of 1/(1+5x^2)	\int\:\frac{1}{1+5x^{2}}dx
derivative of sqrt(3-5x)	derivative\:\sqrt{3-5x}
derivative of f(x)=ax^2+bx	derivative\:f(x)=ax^{2}+bx
integral of 2/(x^{0.85)}	\int\:\frac{2}{x^{0.85}}dx
(\partial)/(\partial x)(2xy+xf(x,y)(y/x))	\frac{\partial\:}{\partial\:x}(2xy+xf(x,y)(\frac{y}{x}))
(\partial)/(\partial y)(3+2xy)	\frac{\partial\:}{\partial\:y}(3+2xy)
area 5x,3x^2	area\:5x,3x^{2}
(\partial)/(\partial x)(2cos(x^2+y^2))	\frac{\partial\:}{\partial\:x}(2\cos(x^{2}+y^{2}))
derivative of sqrt(x+13)	\frac{d}{dx}(\sqrt{x+13})
limit as x approaches infinity of ln\|x\|	\lim\:_{x\to\:\infty\:}(\ln\left\|x\right\|)
y^{''}+81y=0,y(0)=4,y^'(0)=7	y^{\prime\:\prime\:}+81y=0,y(0)=4,y^{\prime\:}(0)=7
implicit (dy)/(dx), y/x =0	implicit\:\frac{dy}{dx},\frac{y}{x}=0
limit as x approaches 0 of ln(x)sin(x)	\lim\:_{x\to\:0}(\ln(x)\sin(x))
integral from-2 to 7 of ()((t-7)(1-t))	\int\:_{-2}^{7}\frac{d}{dt}((t-7)(1-t))dt
integral from 0 to 0.6 of 500x	\int\:_{0}^{0.6}500xdx
derivative of (8x^3-5x+2)^pi	derivative\:(8x^{3}-5x+2)^{π}
tangent of y=(1+x)/(1+e^x),(0, 1/2)	tangent\:y=\frac{1+x}{1+e^{x}},(0,\frac{1}{2})
limit as x approaches 0+of 3xln(x)	\lim\:_{x\to\:0+}(3x\ln(x))
derivative of sqrt(3x)ln(15x)	derivative\:\sqrt{3x}\ln(15x)
area x^2+2x+1,2x+5,[-2,2]	area\:x^{2}+2x+1,2x+5,[-2,2]
derivative of f(x)=2log_{5}(x)	derivative\:f(x)=2\log_{5}(x)
integral of 8/(2+8x)	\int\:\frac{8}{2+8x}dx
derivative of 10sqrt(6x^9+9x^6)	derivative\:10\sqrt{6x^{9}+9x^{6}}
limit as x approaches 2-of (x^2)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{x^{2}}{x^{2}-4})
(\partial)/(\partial y)(xe^y-ye^x)	\frac{\partial\:}{\partial\:y}(xe^{y}-ye^{x})
(dy)/(dx)=2y-xy^2	\frac{dy}{dx}=2y-xy^{2}
integral of-5/(sqrt(12-12x^2))	\int\:-\frac{5}{\sqrt{12-12x^{2}}}dx
derivative of (x^2+5/(x^2+6x))	\frac{d}{dx}(\frac{x^{2}+5}{x^{2}+6x})
tangent of y=x^2-2x-3,(2,-3)	tangent\:y=x^{2}-2x-3,(2,-3)
sum from n=0 to infinity of cn(x-8)^n	\sum\:_{n=0}^{\infty\:}cn(x-8)^{n}
derivative of x/(3sqrt(x^2+1))-1/8	derivative\:\frac{x}{3\sqrt{x^{2}+1}}-\frac{1}{8}
(\partial)/(\partial t)(t/2)	\frac{\partial\:}{\partial\:t}(\frac{t}{2})
derivative of 2x^3-6	\frac{d}{dx}(2x^{3}-6)

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