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Popular Calculus Problems

(\partial)/(\partial t)(e^{-6t}cos(pix))	\frac{\partial\:}{\partial\:t}(e^{-6t}\cos(πx))
f(x)=e^{x-1}	f(x)=e^{x-1}
derivative of (9(5^x))/(x^5)	derivative\:\frac{9(5^{x})}{x^{5}}
integral of (ln(x^2))/x	\int\:\frac{\ln(x^{2})}{x}dx
integral from 0 to 1 of (arctan(2x))	\int\:_{0}^{1}(\arctan(2x))dx
derivative of f(x)=7x^2tan(x)	derivative\:f(x)=7x^{2}\tan(x)
xy^'+y=7xy^2	xy^{\prime\:}+y=7xy^{2}
integral of 6xsqrt(3x^2+2)	\int\:6x\sqrt{3x^{2}+2}dx
derivative of f(x)=x+7	derivative\:f(x)=x+7
(\partial)/(\partial x)(3x^2y^2-2)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}-2)
derivative of e^{-2x}(1-x)	\frac{d}{dx}(e^{-2x}(1-x))
derivative of 10(3x^2+7x-3^{10})	\frac{d}{dx}(10(3x^{2}+7x-3)^{10})
integral of (2x)/(sqrt((4-x)^3))	\int\:\frac{2x}{\sqrt{(4-x)^{3}}}dx
derivative of 5ln(x^5)	\frac{d}{dx}(5\ln(x^{5}))
(e^{sqrt(x)})^'	(e^{\sqrt{x}})^{\prime\:}
integral of 4x^{-6/7}	\int\:4x^{-\frac{6}{7}}dx
xy^'+(2x-3)y=4x^4	xy^{\prime\:}+(2x-3)y=4x^{4}
inverse oflaplace ((s+1))/((s+2)(s-3))	inverselaplace\:\frac{(s+1)}{(s+2)(s-3)}
4y-y^{''}=10e^{-3x}	4y-y^{\prime\:\prime\:}=10e^{-3x}
integral of ln(x)+1	\int\:\ln(x)+1dx
integral of 2sin(x)+cos(x)	\int\:2\sin(x)+\cos(x)dx
integral from-1 to 2 of (x^2+1)	\int\:_{-1}^{2}(x^{2}+1)dx
integral of xarcsin(2x^2)	\int\:x\arcsin(2x^{2})dx
limit as n approaches infinity of 1^n	\lim\:_{n\to\:\infty\:}(1^{n})
integral of (10x)/(x^2+1)	\int\:\frac{10x}{x^{2}+1}dx
derivative of ({f}(x)/x)	\frac{d}{dx}(\frac{{f}(x)}{x})
tangent of f(x)=6x^2+2x-7,\at x=-4	tangent\:f(x)=6x^{2}+2x-7,\at\:x=-4
derivative of (1+e^{x^2})^3	derivative\:(1+e^{x^{2}})^{3}
(\partial)/(\partial z)(x+y/z)	\frac{\partial\:}{\partial\:z}(x+\frac{y}{z})
sum from n=0 to infinity of 1/(n+4)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+4}
integral of x(x^2+1)^{10}	\int\:x(x^{2}+1)^{10}dx
area y=6-x^2,y=x	area\:y=6-x^{2},y=x
integral of 3/(17x^2)	\int\:\frac{3}{17x^{2}}dx
sum from n=0 to infinity of n/n	\sum\:_{n=0}^{\infty\:}\frac{n}{n}
derivative of 3x^2+(16x/3-2)	\frac{d}{dx}(3x^{2}+\frac{16x}{3}-2)
(\partial)/(\partial y)(xcos(xy))	\frac{\partial\:}{\partial\:y}(x\cos(xy))
(dy)/(dt)=((4ty^2))/(t^2+1),y(0)= 1/4	\frac{dy}{dt}=\frac{(4ty^{2})}{t^{2}+1},y(0)=\frac{1}{4}
integral of x^2-4x-5	\int\:x^{2}-4x-5dx
area y=sqrt(9-x^2),-1<= x<= 1	area\:y=\sqrt{9-x^{2}},-1\le\:x\le\:1
integral of 2x^2sin(x/3)	\int\:2x^{2}\sin(\frac{x}{3})dx
derivative of sqrt(9x-18)	\frac{d}{dx}(\sqrt{9x-18})
integral of sin(4x)ln(sin(4x))	\int\:\sin(4x)\ln(\sin(4x))dx
integral of (3t+t^2)sin(2t)	\int\:(3t+t^{2})\sin(2t)dt
derivative of 6xsqrt(x^3+3x)	\frac{d}{dx}(6x\sqrt{x^{3}+3x})
(\partial)/(\partial x)(xh)	\frac{\partial\:}{\partial\:x}(xh)
y^'+6y=t+e^{-2t}	y^{\prime\:}+6y=t+e^{-2t}
derivative of (5x/(1+2x^2))	\frac{d}{dx}(\frac{5x}{1+2x^{2}})
limit as x approaches 0+of (sin^2(x))/x	\lim\:_{x\to\:0+}(\frac{\sin^{2}(x)}{x})
tangent of x^2+xy-y^2=-1,(1,2)	tangent\:x^{2}+xy-y^{2}=-1,(1,2)
derivative of (x-7)(2x+4)	derivative\:(x-7)(2x+4)
limit as x approaches 1 of x/(x^2+4)	\lim\:_{x\to\:1}(\frac{x}{x^{2}+4})
derivative of y=(4x^3+5)(x^4-3x)	derivative\:y=(4x^{3}+5)(x^{4}-3x)
sum from n=1 to infinity of n+1/(n^2)	\sum\:_{n=1}^{\infty\:}n+\frac{1}{n^{2}}
(dy)/(dx)=2sqrt(x)	\frac{dy}{dx}=2\sqrt{x}
integral from 1 to 5 of pi(x-1)	\int\:_{1}^{5}π(x-1)dx
sum from n=1 to infinity of \sqrt[n]{7}	\sum\:_{n=1}^{\infty\:}\sqrt[n]{7}
integral of ((y+1)^2)/y	\int\:\frac{(y+1)^{2}}{y}dy
derivative of sqrt(2-x^2)	derivative\:\sqrt{2-x^{2}}
d/(dy)((x^3-y^3)/(x^2+y^2))	\frac{d}{dy}(\frac{x^{3}-y^{3}}{x^{2}+y^{2}})
derivative of x^2+x-4	\frac{d}{dx}(x^{2}+x-4)
derivative of sqrt(x^2-3x)	\frac{d}{dx}(\sqrt{x^{2}-3x})
integral from 1 to 5 of 3x^2+1/(12x^2)	\int\:_{1}^{5}3x^{2}+\frac{1}{12x^{2}}dx
t=y+y^'	t=y+y^{\prime\:}
integral of 5-x^2	\int\:5-x^{2}dx
integral from-3 to 3 of (2x^4-3x^3)	\int\:_{-3}^{3}(2x^{4}-3x^{3})dx
integral of xex	\int\:xexdx
derivative of sin(sin(sin(x)))	derivative\:\sin(\sin(\sin(x)))
limit as x approaches-5+of-(9x)/(x+5)	\lim\:_{x\to\:-5+}(-\frac{9x}{x+5})
derivative of (3e^x/(2e^x+1))	\frac{d}{dx}(\frac{3e^{x}}{2e^{x}+1})
(\partial)/(\partial x)(xe^{2y}sin(6z))	\frac{\partial\:}{\partial\:x}(xe^{2y}\sin(6z))
integral from 0 to t of t^2e^{-3t}	\int\:_{0}^{t}t^{2}e^{-3t}dt
(\partial)/(\partial x)(2(y-1)(x+1))	\frac{\partial\:}{\partial\:x}(2(y-1)(x+1))
integral from-1 to 7 of 3x+7-x^2+3x	\int\:_{-1}^{7}3x+7-x^{2}+3xdx
derivative of (x^2+3x/(x-1))	\frac{d}{dx}(\frac{x^{2}+3x}{x-1})
derivative of f(x)=6\sqrt[3]{x^2}	derivative\:f(x)=6\sqrt[3]{x^{2}}
(dN)/(dt)+N=Nte^{t+2}	\frac{dN}{dt}+N=Nte^{t+2}
integral of sqrt((x^4)/(x^3-1))	\int\:\sqrt{\frac{x^{4}}{x^{3}-1}}dx
area y= 4/(sqrt(4-x^2)),(0,1)	area\:y=\frac{4}{\sqrt{4-x^{2}}},(0,1)
ty^'+y=8	ty^{\prime\:}+y=8
derivative of (2t)/(t^2+4)	derivative\:\frac{2t}{t^{2}+4}
slope ofintercept (5,-3),(0,-9)	slopeintercept\:(5,-3),(0,-9)
(\partial)/(\partial y)(e^{3x}*tan(y))	\frac{\partial\:}{\partial\:y}(e^{3x}\cdot\:\tan(y))
derivative of (x^2+4^2(2x^3-1)^3)	\frac{d}{dx}((x^{2}+4)^{2}(2x^{3}-1)^{3})
derivative of f(x)= 2/(1+e^{-x)}	derivative\:f(x)=\frac{2}{1+e^{-x}}
integral of 7sin^5(x)cos^{-3/2}(x)	\int\:7\sin^{5}(x)\cos^{-\frac{3}{2}}(x)dx
integral from 0 to 2 of integral from 0 to 3 of ((x^2y^2)/4)	\int\:_{0}^{2}\int\:_{0}^{3}(\frac{x^{2}y^{2}}{4})dxdy
f(x)=sin(5ln(x))	f(x)=\sin(5\ln(x))
derivative of (sin(5x)/x)	\frac{d}{dx}(\frac{\sin(5x)}{x})
((cos(x))^2)^'	((\cos(x))^{2})^{\prime\:}
integral of x^5ln(3x)	\int\:x^{5}\ln(3x)dx
integral of 12x^2-10x+4	\int\:12x^{2}-10x+4dx
derivative of pi/(2x^5)	\frac{d}{dx}(\frac{π}{2x^{5}})
integral of 3x^2+4	\int\:3x^{2}+4dx
limit as x approaches 3 of sqrt(x^2+7)+5	\lim\:_{x\to\:3}(\sqrt{x^{2}+7}+5)
derivative of y=4x^3sqrt(1-x^2)	derivative\:y=4x^{3}\sqrt{1-x^{2}}
integral of (x+4)/(x-4)	\int\:\frac{x+4}{x-4}dx
d/(dt)(6-3t^2)	\frac{d}{dt}(6-3t^{2})
(\partial)/(\partial y)((xy^2)/(t+2z))	\frac{\partial\:}{\partial\:y}(\frac{xy^{2}}{t+2z})
(\partial)/(\partial y)(z-xsin(y)-4)	\frac{\partial\:}{\partial\:y}(z-x\sin(y)-4)
limit as x approaches-1 of 1-2x	\lim\:_{x\to\:-1}(1-2x)

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