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Popular Calculus Problems

(\partial)/(\partial x)(1/2 (x^2+10y^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}(x^{2}+10y^{2}))
f(x)=x-cos(x)	f(x)=x-\cos(x)
integral from 0 to 6 of 2.3^tsin(t/2)	\int\:_{0}^{6}2.3^{t}\sin(\frac{t}{2})dt
integral of ((2x+4))/(x^2+4x+5)	\int\:\frac{(2x+4)}{x^{2}+4x+5}dx
integral of (x^2+2x+3)/(x^3+3x^2+9x+1)	\int\:\frac{x^{2}+2x+3}{x^{3}+3x^{2}+9x+1}dx
integral of 1/(2x^2+x)	\int\:\frac{1}{2x^{2}+x}dx
area sin(x),-sin(x),[0,4]	area\:\sin(x),-\sin(x),[0,4]
integral of (10x^3-5x^2+4x)/(x^2)	\int\:\frac{10x^{3}-5x^{2}+4x}{x^{2}}dx
derivative of tanh(2x-3)	\frac{d}{dx}(\tanh(2x-3))
tangent of f(x)=x^2+x,(1,2)	tangent\:f(x)=x^{2}+x,(1,2)
slope ofintercept (-1,-4),(0,2)	slopeintercept\:(-1,-4),(0,2)
area-x^2+3x+1,-x-1,[0,4]	area\:-x^{2}+3x+1,-x-1,[0,4]
integral of (-3)/x	\int\:\frac{-3}{x}dx
integral of (4t-3)/(t+1)	\int\:\frac{4t-3}{t+1}dt
tangent of f(x)=x^4+5x^2-x,(1,5)	tangent\:f(x)=x^{4}+5x^{2}-x,(1,5)
integral of (4x+3)/(x^2+4)	\int\:\frac{4x+3}{x^{2}+4}dx
(x^4-x+y)dx-xdy=0	(x^{4}-x+y)dx-xdy=0
derivative of ln(xsqrt(x^2+1))	derivative\:\ln(x\sqrt{x^{2}+1})
tangent of f(x)=6x-6x	tangent\:f(x)=6x-6x
integral from 1 to 2 of xe^{x^2}	\int\:_{1}^{2}xe^{x^{2}}dx
(dy)/(dx)=(4y)	\frac{dy}{dx}=(4y)
derivative of (3x^2+4(2x-3))	\frac{d}{dx}((3x^{2}+4)(2x-3))
integral of 5/x+e^x	\int\:\frac{5}{x}+e^{x}dx
tangent of y=5+5x^2-2x^3	tangent\:y=5+5x^{2}-2x^{3}
integral of (x-5)^2e^x	\int\:(x-5)^{2}e^{x}dx
limit as x approaches 8+of 1/((x-8)^2)	\lim\:_{x\to\:8+}(\frac{1}{(x-8)^{2}})
y^'+3y=3	y^{\prime\:}+3y=3
derivative of 5x+3sqrt(x)	derivative\:5x+3\sqrt{x}
inverse oflaplace (12s)/((132s+30s^2))	inverselaplace\:\frac{12s}{(132s+30s^{2})}
area y=2x,y=4x^2	area\:y=2x,y=4x^{2}
integral of x^2-x^4	\int\:x^{2}-x^{4}dx
derivative of sin^2(xcos^2(x))	\frac{d}{dx}(\sin^{2}(x)\cos^{2}(x))
derivative of (2x^2+4x-3/(x-5))	\frac{d}{dx}(\frac{2x^{2}+4x-3}{x-5})
derivative of e^{-9x}	derivative\:e^{-9x}
derivative of sec^2(6x)	\frac{d}{dx}(\sec^{2}(6x))
derivative of c_{1}e^x+c_{2}e^{2x}	\frac{d}{dx}(c_{1}e^{x}+c_{2}e^{2x})
(dx}{dt}=t^5-\frac{2x)/t	\frac{dx}{dt}=t^{5}-\frac{2x}{t}
integral from 0 to pi/6 of xsin(x+y)	\int\:_{0}^{\frac{π}{6}}x\sin(x+y)dx
derivative of ln(1+10x)	\frac{d}{dx}(\ln(1+10x))
integral of 1/(sqrt(x+1)+\sqrt[4]{x+1)}	\int\:\frac{1}{\sqrt{x+1}+\sqrt[4]{x+1}}dx
limit as x approaches 4+of 2x	\lim\:_{x\to\:4+}(2x)
limit as x approaches 0+of cot(x)	\lim\:_{x\to\:0+}(\cot(x))
integral from 0 to 2 of (2x+5)	\int\:_{0}^{2}(2x+5)dx
(0^2e^{0+3})^'	(0^{2}e^{0+3})^{\prime\:}
derivative of (x^5/(2-x^4))	\frac{d}{dx}(\frac{x^{5}}{2-x^{4}})
3y^{''}-30y^'+72y=6sin(4x)	3y^{\prime\:\prime\:}-30y^{\prime\:}+72y=6\sin(4x)
integral of (3x^2+6)/((x^2-2x+2)^2)	\int\:\frac{3x^{2}+6}{(x^{2}-2x+2)^{2}}dx
derivative of sin(x^3+3xy)	\frac{d}{dx}(\sin(x^{3})+3xy)
tangent of f(x)= x/(x+3),\at x=1	tangent\:f(x)=\frac{x}{x+3},\at\:x=1
derivative of f(x)=e^{6x}cos(9x)	derivative\:f(x)=e^{6x}\cos(9x)
derivative of ln(2+x^2)	\frac{d}{dx}(\ln(2+x^{2}))
integral of cos(5x)	\int\:\cos(5x)dx
integral of sqrt(9-x^2)	\int\:\sqrt{9-x^{2}}dx
laplacetransform g(t)=sin(2t)sin(t)	laplacetransform\:g(t)=\sin(2t)\sin(t)
derivative of tan(ln(ax+b))	\frac{d}{dx}(\tan(\ln(ax+b)))
derivative of x^3-1/(x^2)	\frac{d}{dx}(x^{3}-\frac{1}{x^{2}})
limit as x approaches-infinity of xe^x-1	\lim\:_{x\to\:-\infty\:}(xe^{x}-1)
derivative of (x^3)/(5-x^2)	derivative\:\frac{x^{3}}{5-x^{2}}
derivative of 1/3 x^3+7x^2+50x	\frac{d}{dx}(\frac{1}{3}x^{3}+7x^{2}+50x)
integral of (y^4)/(sqrt(y^2-9))	\int\:\frac{y^{4}}{\sqrt{y^{2}-9}}dy
integral of (1+sin(x))	\int\:(1+\sin(x))dx
(\partial)/(\partial x)(2x^2-3y^2-2x)	\frac{\partial\:}{\partial\:x}(2x^{2}-3y^{2}-2x)
(\partial)/(\partial x)(y^2+1)	\frac{\partial\:}{\partial\:x}(y^{2}+1)
integral of tan(x/(sqrt(2)))	\int\:\tan(\frac{x}{\sqrt{2}})dx
d/(dt)(tcos(6t))	\frac{d}{dt}(t\cos(6t))
(\partial)/(\partial x)(e^{2x^3-3y})	\frac{\partial\:}{\partial\:x}(e^{2x^{3}-3y})
integral of (x^2-8x-1)/((x-1)^2(x^2+1))	\int\:\frac{x^{2}-8x-1}{(x-1)^{2}(x^{2}+1)}dx
derivative of 2x+8	\frac{d}{dx}(2x+8)
derivative of [arctan(3x]^2)	\frac{d}{dx}([\arctan(3x)]^{2})
derivative of 1680(2x+5)^4	derivative\:1680(2x+5)^{4}
y^{''}+y=5e^{-8x}	y^{\prime\:\prime\:}+y=5e^{-8x}
integral of 0.007e^{-0.007x}	\int\:0.007e^{-0.007x}dx
sum from n=1 to infinity of 2(2/3)^{n-1}	\sum\:_{n=1}^{\infty\:}2(\frac{2}{3})^{n-1}
derivative of cos(xln(cos(x)))	\frac{d}{dx}(\cos(x)\ln(\cos(x)))
(dy)/(dt)=2y+2t^2-10/3 t	\frac{dy}{dt}=2y+2t^{2}-\frac{10}{3}t
integral of 2z	\int\:2zdz
maclaurin x^5sin(x)	maclaurin\:x^{5}\sin(x)
derivative of (sin(x)/(cos^2(x)))	\frac{d}{dx}(\frac{\sin(x)}{\cos^{2}(x)})
derivative of 4-x^{2/3}	\frac{d}{dx}(4-x^{\frac{2}{3}})
derivative of x^{4/3}-5	\frac{d}{dx}(x^{\frac{4}{3}}-5)
integral from-1 to 3 of (1+4x)	\int\:_{-1}^{3}(1+4x)dx
derivative of f(x)=arctan(cos(x))	derivative\:f(x)=\arctan(\cos(x))
derivative of 3x^3+5x	\frac{d}{dx}(3x^{3}+5x)
derivative of sqrt(x)(2-x^2)	\frac{d}{dx}(\sqrt{x}(2-x)^{2})
(\partial)/(\partial x)(xe^{-3z+2y})	\frac{\partial\:}{\partial\:x}(xe^{-3z+2y})
derivative of arccos(3x^2)	derivative\:\arccos(3x^{2})
derivative of e^{1-cos(x})	\frac{d}{dx}(e^{1-\cos(x)})
derivative of xe^2	\frac{d}{dx}(xe^{2})
derivative of 4x(2x-3)^7	derivative\:4x(2x-3)^{7}
(\partial)/(\partial x)(x^4sin(2x))	\frac{\partial\:}{\partial\:x}(x^{4}\sin(2x))
laplacetransform e^{-(t-1)}	laplacetransform\:e^{-(t-1)}
derivative of x-ln(sec(x+tan(x)))	\frac{d}{dx}(x-\ln(\sec(x)+\tan(x)))
derivative of (-2x^3+x^2-2x-1)x^3	derivative\:(-2x^{3}+x^{2}-2x-1)x^{3}
derivative of 2e^{5x}	\frac{d}{dx}(2e^{5x})
integral of 2xy+2x	\int\:2xy+2xdx
limit as t approaches 0 of (1-e^{-2t})/t	\lim\:_{t\to\:0}(\frac{1-e^{-2t}}{t})
f(t)=sin^2(t)	f(t)=\sin^{2}(t)
limit as x approaches 3 of (x^2+x)/(x+3)	\lim\:_{x\to\:3}(\frac{x^{2}+x}{x+3})
integral of (13)/(x^2-1)	\int\:\frac{13}{x^{2}-1}dx
limit as x approaches 0 of xe^{-x}	\lim\:_{x\to\:0}(xe^{-x})

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