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Popular Calculus Problems

tangent of f(x)=x^2,(0,-4)	tangent\:f(x)=x^{2},(0,-4)
derivative of 3x^3+4/x	derivative\:3x^{3}+\frac{4}{x}
(\partial)/(\partial x)(xln(y)-y^22^{xy})	\frac{\partial\:}{\partial\:x}(x\ln(y)-y^{2}2^{xy})
y^{''}+9y=-sin(3x)	y^{\prime\:\prime\:}+9y=-\sin(3x)
integral from 0 to 1 of 1/(x^2-2x+2)	\int\:_{0}^{1}\frac{1}{x^{2}-2x+2}dx
(\partial)/(\partial φ)(ρsin(φ)sin(θ))	\frac{\partial\:}{\partial\:φ}(ρ\sin(φ)\sin(θ))
y^{''}-4y^'+4y=(e^{2x})/(x^2)	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=\frac{e^{2x}}{x^{2}}
limit as x approaches a of sin(x)	\lim\:_{x\to\:a}(\sin(x))
integral from 6 to 8 of 1/(x^2-1)	\int\:_{6}^{8}\frac{1}{x^{2}-1}dx
limit as x approaches 0 of xsec(x)csc(x)	\lim\:_{x\to\:0}(x\sec(x)\csc(x))
(dy)/(dx)+y+3sin(x)=0	\frac{dy}{dx}+y+3\sin(x)=0
integral from 0 to pi/3 of (2sec^2(x))	\int\:_{0}^{\frac{π}{3}}(2\sec^{2}(x))dx
tangent of y= 7/(sqrt(x)),(4, 7/2)	tangent\:y=\frac{7}{\sqrt{x}},(4,\frac{7}{2})
derivative of sqrt(50-x^2)-x	\frac{d}{dx}(\sqrt{50-x^{2}}-x)
limit as x approaches pi/2 of tan(x)	\lim\:_{x\to\:\frac{π}{2}}(\tan(x))
derivative of 64	\frac{d}{dx}(64)
area x=10y-y^2,x=y^2-4y	area\:x=10y-y^{2},x=y^{2}-4y
integral of (-1000)/(x^2)	\int\:\frac{-1000}{x^{2}}dx
inverse oflaplace (s^2+s)/(s^2+s+1)	inverselaplace\:\frac{s^{2}+s}{s^{2}+s+1}
y^{''}-3y^'+7y=xe^x	y^{\prime\:\prime\:}-3y^{\prime\:}+7y=xe^{x}
integral of 8/(sqrt(12-x^2-4x))	\int\:\frac{8}{\sqrt{12-x^{2}-4x}}dx
derivative of 3x^2	derivative\:3x^{2}
integral of (2x+1)^7	\int\:(2x+1)^{7}dx
derivative of ln^2(sin(2x))	\frac{d}{dx}(\ln^{2}(\sin(2x)))
derivative of sqrt(10-x)	derivative\:\sqrt{10-x}
d/(dy)((1/(y^2)-3/(y^4))(y+7y^3))	\frac{d}{dy}((\frac{1}{y^{2}}-\frac{3}{y^{4}})(y+7y^{3}))
limit as x approaches infinity of e^x	\lim\:_{x\to\:\infty\:}(e^{x})
integral from 0 to 2 of (x^3+1)^{1/2}x^2	\int\:_{0}^{2}(x^{3}+1)^{\frac{1}{2}}x^{2}dx
integral of 3(sin(2x))/(sin(x))	\int\:3\frac{\sin(2x)}{\sin(x)}dx
slope of (-5,-2),(5,14)	slope\:(-5,-2),(5,14)
limit as x approaches-1/4 of 2	\lim\:_{x\to\:-\frac{1}{4}}(2)
limit as x approaches a of [2f(3)-3g(4)]	\lim\:_{x\to\:a}([2f(3)-3g(4)])
y'(t)	y\prime\:(t)
integral of 3/(2x+1)	\int\:\frac{3}{2x+1}dx
limit as u approaches 0 of 6-u^2	\lim\:_{u\to\:0}(6-u^{2})
integral of (sin(θ))/(cos^3(θ)+cos(θ))	\int\:\frac{\sin(θ)}{\cos^{3}(θ)+\cos(θ)}dθ
derivative of cos(2t)	derivative\:\cos(2t)
limit as x approaches-3 of-x^2+5x-1	\lim\:_{x\to\:-3}(-x^{2}+5x-1)
limit as x approaches+0 of x^2cos(1/x)	\lim\:_{x\to\:+0}(x^{2}\cos(\frac{1}{x}))
derivative of-3e^{-2x}	\frac{d}{dx}(-3e^{-2x})
integral from 0 to 4 of (6t)/((t-5)^2)	\int\:_{0}^{4}\frac{6t}{(t-5)^{2}}dt
integral of (-2x^5-5x^3+3x^2+1-4e^x)	\int\:(-2x^{5}-5x^{3}+3x^{2}+1-4e^{x})dx
(dy)/(dx)+(4/(76+3x))y=4.2	\frac{dy}{dx}+(\frac{4}{76+3x})y=4.2
derivative of 7sqrt(x-2)	\frac{d}{dx}(7\sqrt{x-2})
derivative of f(x)=5e^x+4/(\sqrt[3]{x)}	derivative\:f(x)=5e^{x}+\frac{4}{\sqrt[3]{x}}
d/(dt)(4sin(t))	\frac{d}{dt}(4\sin(t))
y^{''}+11y^'+18y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+11y^{\prime\:}+18y=0,y(0)=1,y^{\prime\:}(0)=0
derivative of f(x)=-3/2 x^2	derivative\:f(x)=-\frac{3}{2}x^{2}
integral from-1 to 0 of te^{-j^2pift}	\int\:_{-1}^{0}te^{-j^{2}πft}dt
derivative of 6x^2+6x-36	\frac{d}{dx}(6x^{2}+6x-36)
(x^{1/2})^'	(x^{\frac{1}{2}})^{\prime\:}
limit as x approaches 0 of a^x-b^x	\lim\:_{x\to\:0}(a^{x}-b^{x})
derivative of 2x*ln(x)	\frac{d}{dx}(2x\cdot\:\ln(x))
derivative of 4arctan(x)	\frac{d}{dx}(4\arctan(x))
x^2y^{''}-7xy^'+15y=0	x^{2}y^{\prime\:\prime\:}-7xy^{\prime\:}+15y=0
integral of 10xe^{0.1x^2}	\int\:10xe^{0.1x^{2}}dx
(d^2y)/(dx^2)=-25y	\frac{d^{2}y}{dx^{2}}=-25y
laplacetransform (e^{2t}-e^1)/2	laplacetransform\:\frac{e^{2t}-e^{1}}{2}
integral from 0 to 1 of pi(x)^2	\int\:_{0}^{1}π(x)^{2}dx
limit as h approaches 0 of sqrt(3h-1)	\lim\:_{h\to\:0}(\sqrt{3h-1})
x^3+y^2sqrt(x^4+2)y^'=0	x^{3}+y^{2}\sqrt{x^{4}+2}y^{\prime\:}=0
integral of 1/(4sqrt(x))	\int\:\frac{1}{4\sqrt{x}}dx
derivative of 5/(9w^6)+5\sqrt[4]{w}	derivative\:\frac{5}{9w^{6}}+5\sqrt[4]{w}
integral from 1 to 9 of (x-1)^{-2/3}	\int\:_{1}^{9}(x-1)^{-\frac{2}{3}}dx
integral of 2/3 x^{3/2}	\int\:\frac{2}{3}x^{\frac{3}{2}}dx
integral of (x^2)/(y^2)	\int\:\frac{x^{2}}{y^{2}}dy
integral of 10x^4-sec^2(x)	\int\:10x^{4}-\sec^{2}(x)dx
derivative of x^3(3x^6-5x^2+4)	\frac{d}{dx}(x^{3}(3x^{6}-5x^{2}+4))
area y=x,y=sqrt(x),x=4	area\:y=x,y=\sqrt{x},x=4
integral of 1/3 (1-x^2)^3	\int\:\frac{1}{3}(1-x^{2})^{3}dx
cos(x)(dy)/(dx)+(sin(x))y=1	\cos(x)\frac{dy}{dx}+(\sin(x))y=1
(\partial)/(\partial y)(e^{x^2+y^2}sin(xy))	\frac{\partial\:}{\partial\:y}(e^{x^{2}+y^{2}}\sin(xy))
integral of (5+5sqrt(x+5))/(sqrt(x+5))	\int\:\frac{5+5\sqrt{x+5}}{\sqrt{x+5}}dx
(x^2+1)(dy)/(dx)+5x(y-1)=0	(x^{2}+1)\frac{dy}{dx}+5x(y-1)=0
2y^{''}-11y^'-6y=0	2y^{\prime\:\prime\:}-11y^{\prime\:}-6y=0
integral from 0 to 1 of 7 1/(x^p)	\int\:_{0}^{1}7\frac{1}{x^{p}}dx
limit as x approaches 3 of x^3	\lim\:_{x\to\:3}(x^{3})
integral of (x+2)/(2sqrt(x+2))	\int\:\frac{x+2}{2\sqrt{x+2}}dx
limit as x approaches 2-of (9x)/(x-2)	\lim\:_{x\to\:2-}(\frac{9x}{x-2})
(\partial)/(\partial y)(4x+9y-360)	\frac{\partial\:}{\partial\:y}(4x+9y-360)
derivative of ((2x+1)(x^3+3))/x	derivative\:\frac{(2x+1)(x^{3}+3)}{x}
integral of-2e^{2x}	\int\:-2e^{2x}dx
integral of (e^{4x})/(sqrt(25-e^{2x))}	\int\:\frac{e^{4x}}{\sqrt{25-e^{2x}}}dx
(\partial)/(\partial x)(ln(x^2+2y^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+2y^{2}))
(dy)/(dx)= y/((1+x)(2+x))	\frac{dy}{dx}=\frac{y}{(1+x)(2+x)}
derivative of (x^2/(4-x^2))	\frac{d}{dx}(\frac{x^{2}}{4-x^{2}})
derivative of ((x-2/(x+2))^2)	\frac{d}{dx}((\frac{x-2}{x+2})^{2})
(\partial)/(\partial x)(40sqrt(x))	\frac{\partial\:}{\partial\:x}(40\sqrt{x})
derivative of ln(\sqrt[8]{x})	derivative\:\ln(\sqrt[8]{x})
inverse oflaplace 2/((s+1)(s^2+2^2))	inverselaplace\:\frac{2}{(s+1)(s^{2}+2^{2})}
laplacetransform 3cos(5t)	laplacetransform\:3\cos(5t)
derivative of (ln(4x)/(ln(2x)))	\frac{d}{dx}(\frac{\ln(4x)}{\ln(2x)})
derivative of x^4+225-34x^2	\frac{d}{dx}(x^{4}+225-34x^{2})
integral of (4sqrt(ln^2(x)+9))/x	\int\:\frac{4\sqrt{\ln^{2}(x)+9}}{x}dx
derivative of 7ln(cos(x))	\frac{d}{dx}(7\ln(\cos(x)))
integral of sin^2(3x)cos^4(3x)	\int\:\sin^{2}(3x)\cos^{4}(3x)dx
limit as x approaches infinity of 4-x	\lim\:_{x\to\:\infty\:}(4-x)
integral of csc^5(2x)	\int\:\csc^{5}(2x)dx
(\partial)/(\partial y)(sqrt(x)ln(t))	\frac{\partial\:}{\partial\:y}(\sqrt{x}\ln(t))
integral of e^{xt}	\int\:e^{xt}dx

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