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Popular Calculus Problems

derivative of tan^2(y)	derivative\:\tan^{2}(y)
(\partial)/(\partial x)(2x^3+3y^2-5xy)	\frac{\partial\:}{\partial\:x}(2x^{3}+3y^{2}-5xy)
integral of (2x)/((x-1)^2)	\int\:\frac{2x}{(x-1)^{2}}dx
limit as x approaches 8 of (7+8)/(7(7))	\lim\:_{x\to\:8}(\frac{7+8}{7(7)})
integral from-pi to pi of sin^{101}(x)	\int\:_{-π}^{π}\sin^{101}(x)dx
2ydx+x(x^2ln(y)-1)dy=0	2ydx+x(x^{2}\ln(y)-1)dy=0
derivative of sec(5x+2)	\frac{d}{dx}(\sec(5x+2))
area y= 1/2 x^3+2,y=x+1,x=0,x=1	area\:y=\frac{1}{2}x^{3}+2,y=x+1,x=0,x=1
integral of 2/((x^2+1)(x+1))	\int\:\frac{2}{(x^{2}+1)(x+1)}dx
(\partial)/(\partial x)(e^{x^2+y^2+2y+5})	\frac{\partial\:}{\partial\:x}(e^{x^{2}+y^{2}+2y+5})
limit as x approaches 2 of (-2x^2)/(x-2)	\lim\:_{x\to\:2}(\frac{-2x^{2}}{x-2})
integral of (sqrt(x)-2/(sqrt(x)))	\int\:(\sqrt{x}-\frac{2}{\sqrt{x}})dx
limit as x approaches 0 of x^2-8x+9	\lim\:_{x\to\:0}(x^{2}-8x+9)
laplacetransform e^6	laplacetransform\:e^{6}
d/(dz)(1/z)	\frac{d}{dz}(\frac{1}{z})
integral from 7 to infinity of 2/(x^3)	\int\:_{7}^{\infty\:}\frac{2}{x^{3}}dx
derivative of 8-2/3 x	\frac{d}{dx}(8-\frac{2}{3}x)
y^'-((2x)/(1+x^2))y=1	y^{\prime\:}-(\frac{2x}{1+x^{2}})y=1
integral of sin((xy)/3)	\int\:\sin(\frac{xy}{3})dx
integral of x^{4n+2}	\int\:x^{4n+2}dx
(x-3)e^{(-2y)}=(dy)/(dx)	(x-3)e^{(-2y)}=\frac{dy}{dx}
derivative of f(x)=ln(sqrt(x(1-x)))	derivative\:f(x)=\ln(\sqrt{x(1-x)})
integral from 1 to 6 of 1/x	\int\:_{1}^{6}\frac{1}{x}dx
integral of 1/(x(x^4-1))	\int\:\frac{1}{x(x^{4}-1)}dx
(2xy-9x^2)dx+(2y+x^2+1)dy=0	(2xy-9x^{2})dx+(2y+x^{2}+1)dy=0
integral of (4x)/(x^2+2x-3)	\int\:\frac{4x}{x^{2}+2x-3}dx
tangent of f(x)=tan(x),\at x=0	tangent\:f(x)=\tan(x),\at\:x=0
y^{'''}+y^{''}-8y^'-12y=0	y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}-8y^{\prime\:}-12y=0
(t(x)-t(x)^3)v'+2v=0	(t(x)-t(x)^{3})v\prime\:+2v=0
(\partial)/(\partial x)(xye^{x-y})	\frac{\partial\:}{\partial\:x}(xye^{x-y})
derivative of (sqrt(7))/(x^6)	derivative\:\frac{\sqrt{7}}{x^{6}}
derivative of-1/((x+1^2))	\frac{d}{dx}(-\frac{1}{(x+1)^{2}})
3(1+x^2)(dy)/(dx)=2xy^4	3(1+x^{2})\frac{dy}{dx}=2xy^{4}
integral of 1/(sqrt(4-9x^2))	\int\:\frac{1}{\sqrt{4-9x^{2}}}dx
limit as x approaches 3 of 6-2x	\lim\:_{x\to\:3}(6-2x)
integral of 3xln(2x)	\int\:3x\ln(2x)dx
derivative of y=x(6x+1)^5	derivative\:y=x(6x+1)^{5}
limit as x approaches i of x^2+2x	\lim\:_{x\to\:i}(x^{2}+2x)
integral from 0 to tan(x) of 1/(1+t^2)	\int\:_{0}^{\tan(x)}\frac{1}{1+t^{2}}dt
derivative of (x^2-x-2)/(x^2-6x+9)	derivative\:\frac{x^{2}-x-2}{x^{2}-6x+9}
derivative of arctan(5^x)	\frac{d}{dx}(\arctan(5^{x}))
integral of (sqrt(1-\sqrt{x)})/(sqrt(x))	\int\:\frac{\sqrt{1-\sqrt{x}}}{\sqrt{x}}dx
limit as x approaches 6+of ln(x-6)	\lim\:_{x\to\:6+}(\ln(x-6))
derivative of y=sin(x)+xcos(x)	derivative\:y=\sin(x)+x\cos(x)
integral from 0 to 5 of 1/(x^{19/18)}	\int\:_{0}^{5}\frac{1}{x^{\frac{19}{18}}}dx
tangent of f(x)= 3/(x^2),(1,3)	tangent\:f(x)=\frac{3}{x^{2}},(1,3)
derivative of (9x-6^2)	\frac{d}{dx}((9x-6)^{2})
integral of 1/(sqrt(10+4x-x^2))	\int\:\frac{1}{\sqrt{10+4x-x^{2}}}dx
integral of-(2xy)/((x^2+y^2)^2)	\int\:-\frac{2xy}{(x^{2}+y^{2})^{2}}dy
xy^'+3y=((2e^{-2x}))/(x^2)	xy^{\prime\:}+3y=\frac{(2e^{-2x})}{x^{2}}
limit as x approaches infinity of 7+1/x	\lim\:_{x\to\:\infty\:}(7+\frac{1}{x})
tangent of x^3+y^3=9xy,(4,2)	tangent\:x^{3}+y^{3}=9xy,(4,2)
derivative of 1/(\sqrt[4]{x^3})	\frac{d}{dx}(\frac{1}{\sqrt[4]{x^{3}}})
limit as x approaches-1 of-4x^9-2x^6-x^3	\lim\:_{x\to\:-1}(-4x^{9}-2x^{6}-x^{3})
derivative of x+ln\|x^2-4x+3\|	\frac{d}{dx}(x+\ln\left\|x^{2}-4x+3\right\|)
integral of 1/(1+x)	\int\:\frac{1}{1+x}dx
(\partial)/(\partial x)(xsqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(x\sqrt{x^{2}+y^{2}})
area y=3x,y= 3/x	area\:y=3x,y=\frac{3}{x}
(\partial)/(\partial z)(4x^{y/z})	\frac{\partial\:}{\partial\:z}(4x^{\frac{y}{z}})
area 2x-10,[4,8]	area\:2x-10,[4,8]
derivative of cos((sqrt(3))/2 x)	derivative\:\cos(\frac{\sqrt{3}}{2}x)
derivative of 2000(1-x/(600))^2	derivative\:2000(1-\frac{x}{600})^{2}
derivative of ln(sqrt(x^2+19))	\frac{d}{dx}(\ln(\sqrt{x^{2}+19}))
integral of 3/(sqrt(6x-x^2))	\int\:\frac{3}{\sqrt{6x-x^{2}}}dx
tangent of f(x)=sqrt(5x+6),\at a=2	tangent\:f(x)=\sqrt{5x+6},\at\:a=2
derivative of ln(x^2-14x)	\frac{d}{dx}(\ln(x^{2}-14x))
2x^2-80x+y^2+49=0(0)	2x^{2}-80x+y^{2}+49=0(0)
integral from 1 to 2 of 4-x^2	\int\:_{1}^{2}4-x^{2}dx
integral of x^2*sin(4x)	\int\:x^{2}\cdot\:\sin(4x)dx
limit as (x,x^5) approaches (0,0) of (x^5y)/(x^{10)+y^5}	\lim\:_{(x,x^{5})\to\:(0,0)}(\frac{x^{5}y}{x^{10}+y^{5}})
limit as x approaches 2-of (6x)/(x-2)	\lim\:_{x\to\:2-}(\frac{6x}{x-2})
integral of 1/((x^2-1)(x+2))	\int\:\frac{1}{(x^{2}-1)(x+2)}dx
integral of (ke^{-kx})	\int\:(ke^{-kx})dx
y^'+3(tan(3x))y=cos(3x)	y^{\prime\:}+3(\tan(3x))y=\cos(3x)
inverse oflaplace ((12s+5))/(s(s+3))	inverselaplace\:\frac{(12s+5)}{s(s+3)}
derivative of 1/(x^2)-7/(x^4)	derivative\:\frac{1}{x^{2}}-\frac{7}{x^{4}}
integral of (2x-3)e^{x^2-3x}	\int\:(2x-3)e^{x^{2}-3x}dx
derivative of 5ln(2+x)	\frac{d}{dx}(5\ln(2+x))
limit as x approaches 1 of (x^3-1)/(x+1)	\lim\:_{x\to\:1}(\frac{x^{3}-1}{x+1})
integral of (6x^2)	\int\:(6x^{2})dx
derivative of (x^2+3/(cos(x)))	\frac{d}{dx}(\frac{x^{2}+3}{\cos(x)})
tangent of y=arctan(x/4),(4, pi/4)	tangent\:y=\arctan(\frac{x}{4}),(4,\frac{π}{4})
(\partial)/(\partial x)(x^5y)	\frac{\partial\:}{\partial\:x}(x^{5}y)
integral of (4x^2+2x+8)/(x(x^2+2)^2)	\int\:\frac{4x^{2}+2x+8}{x(x^{2}+2)^{2}}dx
limit as x approaches+1 of-3/(x-1)	\lim\:_{x\to\:+1}(-\frac{3}{x-1})
tangent of sqrt(x),\at x=25	tangent\:\sqrt{x},\at\:x=25
(\partial)/(\partial x)(sin(-x)cos(4y))	\frac{\partial\:}{\partial\:x}(\sin(-x)\cos(4y))
y^'=2y+xe^x,y(0)=-1	y^{\prime\:}=2y+xe^{x},y(0)=-1
derivative of (55)/(0.01x^2+1)	derivative\:\frac{55}{0.01x^{2}+1}
integral of tan^4(4t)	\int\:\tan^{4}(4t)dt
(\partial)/(\partial y)(xy+ln(x+y))	\frac{\partial\:}{\partial\:y}(xy+\ln(x+y))
normal of y=2xe^x,(0,0)	normal\:y=2xe^{x},(0,0)
maclaurin cos(pix)	maclaurin\:\cos(πx)
(dy)/(dx)+ycos(x)=3cos(x),y(0)=5	\frac{dy}{dx}+y\cos(x)=3\cos(x),y(0)=5
area y=4x-x^2,y=x	area\:y=4x-x^{2},y=x
tangent of f(x)= 5/(sqrt(x)),\at x= 1/16	tangent\:f(x)=\frac{5}{\sqrt{x}},\at\:x=\frac{1}{16}
integral of ((2t^2+tsqrt(t-1)))/(t^2)	\int\:\frac{(2t^{2}+t\sqrt{t-1})}{t^{2}}dt
(dx)/(dt)+8x=0	\frac{dx}{dt}+8x=0
derivative of 4x(sin(x+cos(x)))	\frac{d}{dx}(4x(\sin(x)+\cos(x)))
(\partial)/(\partial x)(sqrt(xy)+b^{xy})	\frac{\partial\:}{\partial\:x}(\sqrt{xy}+b^{xy})

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