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Popular Calculus Problems

derivative of 2sin(x+sin^2(x))	\frac{d}{dx}(2\sin(x)+\sin^{2}(x))
d/(dX)((X-3)^2+2)	\frac{d}{dX}((X-3)^{2}+2)
f(x)=(3x)/(x^2+1)	f(x)=\frac{3x}{x^{2}+1}
integral of (x-1/x)	\int\:(x-\frac{1}{x})dx
derivative of (x+1)/(x+3)	derivative\:\frac{x+1}{x+3}
y^{''}-3y^'+2y=e^t	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{t}
integral of 4xln(3x)	\int\:4x\ln(3x)dx
((dy)/(dx))-(y/(3x))+(x/(3y))=0	(\frac{dy}{dx})-(\frac{y}{3x})+(\frac{x}{3y})=0
integral of ye^{ty}	\int\:ye^{ty}
(\partial)/(\partial x)((3x)/((x+y)^3))	\frac{\partial\:}{\partial\:x}(\frac{3x}{(x+y)^{3}})
tangent of f(x)=-2sin(x),\at x=(3pi)/4	tangent\:f(x)=-2\sin(x),\at\:x=\frac{3π}{4}
integral of (x^5)/(sqrt(u))	\int\:\frac{x^{5}}{\sqrt{u}}dx
limit as x approaches 0 of sin(0)	\lim\:_{x\to\:0}(\sin(0))
(\partial)/(\partial x)(200(y-x^2))	\frac{\partial\:}{\partial\:x}(200(y-x^{2}))
limit as x approaches-2 of (x-1)/(x^2-4)	\lim\:_{x\to\:-2}(\frac{x-1}{x^{2}-4})
integral of (2x)/(x^3)	\int\:\frac{2x}{x^{3}}dx
integral from-1/2 to 3/2 of x-cos(pix)	\int\:_{-\frac{1}{2}}^{\frac{3}{2}}x-\cos(πx)dx
integral of sin(x)cos(1/2 x)	\int\:\sin(x)\cos(\frac{1}{2}x)dx
(dy)/(dx)=(-y)	\frac{dy}{dx}=(-y)
derivative of (2-x(x+1)^2)	\frac{d}{dx}((2-x)(x+1)^{2})
limit as x approaches 0 of x-1	\lim\:_{x\to\:0}(x-1)
integral of (4x^3-3x^2-8x)/(6x)	\int\:\frac{4x^{3}-3x^{2}-8x}{6x}dx
integral of (sec(3y)tan(36))	\int\:(\sec(3y)\tan(36))dy
integral of (e^{3x})/(4+e^{2x)}	\int\:\frac{e^{3x}}{4+e^{2x}}dx
(dy)/(dx)=-((y^2))/(1+y^2)*e^{-x}	\frac{dy}{dx}=-\frac{(y^{2})}{1+y^{2}}\cdot\:e^{-x}
integral of (-x+2)	\int\:(-x+2)dx
d/(dt)(3cos(3t))	\frac{d}{dt}(3\cos(3t))
integral of (16x+3)	\int\:(16x+3)dx
integral of 1/(xsqrt(9-x^2))	\int\:\frac{1}{x\sqrt{9-x^{2}}}dx
derivative of 1/3 e^{3x}	\frac{d}{dx}(\frac{1}{3}e^{3x})
derivative of sqrt(2cos(x))	\frac{d}{dx}(\sqrt{2\cos(x)})
integral of 6/(sqrt(10x-x^2))	\int\:\frac{6}{\sqrt{10x-x^{2}}}dx
derivative of x^2+(128/x)	\frac{d}{dx}(x^{2}+\frac{128}{x})
y^{'''}+8y^{''}=-6x^2+9x+2	y^{\prime\:\prime\:\prime\:}+8y^{\prime\:\prime\:}=-6x^{2}+9x+2
parity ln(sec(2x)+tan(2x))	parity\:\ln(\sec(2x)+\tan(2x))
y^'=(t+y)2-1	y^{\prime\:}=(t+y)2-1
integral of-6sin(6x)	\int\:-6\sin(6x)dx
integral of (x+2)/(x^2+9)	\int\:\frac{x+2}{x^{2}+9}dx
derivative of (3x^2-x^2(2x+5))	\frac{d}{dx}((3x^{2}-x^{2})(2x+5))
integral of (1-2x)/x	\int\:\frac{1-2x}{x}dx
y(1+x^2)y^'-x(2+y^2)=0,y(0)=sqrt(3)	y(1+x^{2})y^{\prime\:}-x(2+y^{2})=0,y(0)=\sqrt{3}
integral of (x^2)/((4-x^3)^2)	\int\:\frac{x^{2}}{(4-x^{3})^{2}}dx
derivative of f(x)=sin(arccos(x))	derivative\:f(x)=\sin(\arccos(x))
derivative of (3600)/x	derivative\:\frac{3600}{x}
derivative of 5x-x^2	derivative\:5x-x^{2}
(d^2)/(dx^2)(6e^xcos(x))	\frac{d^{2}}{dx^{2}}(6e^{x}\cos(x))
area y=x^2,y=2,y=5	area\:y=x^{2},y=2,y=5
(dx)/(dt)=-x	\frac{dx}{dt}=-x
derivative of y=xβ+e	derivative\:y=xβ+e
derivative of ((x+5/(x^2+2))^2)	\frac{d}{dx}((\frac{x+5}{x^{2}+2})^{2})
limit as x approaches 1+of sqrt(x-1)	\lim\:_{x\to\:1+}(\sqrt{x-1})
limit as x approaches 0+of e^{1/x ln(x)}	\lim\:_{x\to\:0+}(e^{\frac{1}{x}\ln(x)})
integral from 0 to 1 of (7y)/(e^{2y)}	\int\:_{0}^{1}\frac{7y}{e^{2y}}dy
-2y^'+(2y)/x =x^4y^3	-2y^{\prime\:}+\frac{2y}{x}=x^{4}y^{3}
sum from n=1 to infinity of ((n^n))/(n!)	\sum\:_{n=1}^{\infty\:}\frac{(n^{n})}{n!}
derivative of (x^3/((x-1)^2))	\frac{d}{dx}(\frac{x^{3}}{(x-1)^{2}})
integral of sin(2x)cos(2x)tan(2x)	\int\:\sin(2x)\cos(2x)\tan(2x)dx
derivative of 2sin^3(t)	derivative\:2\sin^{3}(t)
y^{''}-5y^'+5y=0	y^{\prime\:\prime\:}-5y^{\prime\:}+5y=0
derivative of (3x+2/(x^2-5x+3))	\frac{d}{dx}(\frac{3x+2}{x^{2}-5x+3})
derivative of cos((8x^2+9^5))	\frac{d}{dx}(\cos((8x^{2}+9)^{5}))
derivative of f(x)g(x)	derivative\:f(x)g(x)
derivative of 2x^2+x-1	derivative\:2x^{2}+x-1
limit as x approaches-6 of ((x^2-36))/(x+6)	\lim\:_{x\to\:-6}(\frac{(x^{2}-36)}{x+6})
integral of (2e^x)/(e^{2x)+1}	\int\:\frac{2e^{x}}{e^{2x}+1}dx
(4x^2+3y^2)dx-2xydy=0	(4x^{2}+3y^{2})dx-2xydy=0
integral from 1 to 5 of x^3ln(4x)	\int\:_{1}^{5}x^{3}\ln(4x)dx
integral of ((x+1)(x-2))/(sqrt(x))	\int\:\frac{(x+1)(x-2)}{\sqrt{x}}dx
(\partial)/(\partial y)(x^2y+yz^3+z^5x)	\frac{\partial\:}{\partial\:y}(x^{2}y+yz^{3}+z^{5}x)
derivative of (x+1/x (x-1/x))	\frac{d}{dx}((x+\frac{1}{x})(x-\frac{1}{x}))
y^{''}+10y^'+25=0	y^{\prime\:\prime\:}+10y^{\prime\:}+25=0
integral of ((100)/(25+(5y)^2)+e^4)	\int\:(\frac{100}{25+(5y)^{2}}+e^{4})dy
derivative of 7\sqrt[4]{-x}	\frac{d}{dx}(7\sqrt[4]{-x})
integral of (x^2)/((x-1))	\int\:\frac{x^{2}}{(x-1)}dx
tangent of f(x)=-2x^2,\at x=-2	tangent\:f(x)=-2x^{2},\at\:x=-2
derivative of sqrt(4x-16)	derivative\:\sqrt{4x-16}
y^{''}+10y^'+20y=0	y^{\prime\:\prime\:}+10y^{\prime\:}+20y=0
inverse oflaplace 1/((s-2)(s+2))	inverselaplace\:\frac{1}{(s-2)(s+2)}
sum from n=0 to infinity of 2(2/3)^n	\sum\:_{n=0}^{\infty\:}2(\frac{2}{3})^{n}
sum from n=1 to infinity of n/2	\sum\:_{n=1}^{\infty\:}\frac{n}{2}
derivative of 5sin^2(x)	derivative\:5\sin^{2}(x)
d/(dt)(8cos(t))	\frac{d}{dt}(8\cos(t))
taylor x^2cos(x)0.1	taylor\:x^{2}\cos(x)0.1
integral of 4/(x^3)	\int\:\frac{4}{x^{3}}dx
(\partial)/(\partial y)(y^2z^3)	\frac{\partial\:}{\partial\:y}(y^{2}z^{3})
integral from 1 to 2 of x^2ln(x)	\int\:_{1}^{2}x^{2}\ln(x)dx
derivative of f(x)=(3x^4+7)^6	derivative\:f(x)=(3x^{4}+7)^{6}
derivative of (2x^3/((x^2+1)^2))	\frac{d}{dx}(\frac{2x^{3}}{(x^{2}+1)^{2}})
derivative of (2xy/(1+x^2))	\frac{d}{dx}(\frac{2xy}{1+x^{2}})
y^'=2e^{2x-y},y(0)=0	y^{\prime\:}=2e^{2x-y},y(0)=0
derivative of x^3-x^2+7x-1	\frac{d}{dx}(x^{3}-x^{2}+7x-1)
integral of 2*cos(x)	\int\:2\cdot\:\cos(x)dx
limit as h approaches 0 of (cos(h)-1)/h	\lim\:_{h\to\:0}(\frac{\cos(h)-1}{h})
limit as x approaches 1 of e^{-x}	\lim\:_{x\to\:1}(e^{-x})
tangent of f(x)=(2x-1)(x+2),\at x=(1.3)	tangent\:f(x)=(2x-1)(x+2),\at\:x=(1.3)
integral of (ln(14x))/(x^6)	\int\:\frac{\ln(14x)}{x^{6}}dx
derivative of ln(t+1)	derivative\:\ln(t+1)
(\partial)/(\partial x)(e^{-3y}cos(-3x))	\frac{\partial\:}{\partial\:x}(e^{-3y}\cos(-3x))
integral of 1/(1+t^2)	\int\:\frac{1}{1+t^{2}}dt
integral from 1 to x of 2(t-1)	\int\:_{1}^{x}2(t-1)dt

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