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Popular Calculus Problems

d/(dt)(tan(sec(cos(t))))	\frac{d}{dt}(\tan(\sec(\cos(t))))
integral of (1+xy)	\int\:(1+xy)dy
sum from n=0 to infinity of 1/(3n+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{3n+1}
(2/x)^'	(\frac{2}{x})^{\prime\:}
integral from-1 to 1 of 1/2 x^2	\int\:_{-1}^{1}\frac{1}{2}x^{2}dx
(dy)/(dx)=y(y^2-1)	\frac{dy}{dx}=y(y^{2}-1)
derivative of y=x^2+2x-4	derivative\:y=x^{2}+2x-4
derivative of y=x^3+3x^2	derivative\:y=x^{3}+3x^{2}
(\partial)/(\partial x)(2cos(y))	\frac{\partial\:}{\partial\:x}(2\cos(y))
derivative of 1/(5x^2)	derivative\:\frac{1}{5x^{2}}
(\partial)/(\partial x)(tan(sqrt(3x)))	\frac{\partial\:}{\partial\:x}(\tan(\sqrt{3x}))
y^{''}-9y^'+20y=0	y^{\prime\:\prime\:}-9y^{\prime\:}+20y=0
limit as x approaches 4 of (x-5)/(x-4)	\lim\:_{x\to\:4}(\frac{x-5}{x-4})
(\partial}{\partial y}(\frac{y^2)/x)	\frac{\partial\:}{\partial\:y}(\frac{y^{2}}{x})
derivative of (x^4/4-9/2 x^2+1)	\frac{d}{dx}(\frac{x^{4}}{4}-\frac{9}{2}x^{2}+1)
integral of (x+y)^2	\int\:(x+y)^{2}dx
limit as x approaches 0 of (sin(4x))/(tan(3x))	\lim\:_{x\to\:0}(\frac{\sin(4x)}{\tan(3x)})
integral from 1 to infinity of 12e^{-6x}	\int\:_{1}^{\infty\:}12e^{-6x}dx
inverse oflaplace (10s^2)/(s^2+9)	inverselaplace\:\frac{10s^{2}}{s^{2}+9}
limit as x approaches 1 of x^2+5	\lim\:_{x\to\:1}(x^{2}+5)
y^'=x+4y-2	y^{\prime\:}=x+4y-2
integral of (x-3)^{-2}	\int\:(x-3)^{-2}dx
limit as x approaches 0 of (2^x-3^x)/x	\lim\:_{x\to\:0}(\frac{2^{x}-3^{x}}{x})
tangent of y=(x^3-16x)^{12},(-4,0)	tangent\:y=(x^{3}-16x)^{12},(-4,0)
derivative of (5x^2)/(sqrt(x))	derivative\:\frac{5x^{2}}{\sqrt{x}}
y^'+y=e^{-x}	y^{\prime\:}+y=e^{-x}
derivative of (8-sec(x))/(tan(x))	derivative\:\frac{8-\sec(x)}{\tan(x)}
integral of (e^{-y})/y	\int\:\frac{e^{-y}}{y}dy
integral from 0 to 2 of (x-1)^2	\int\:_{0}^{2}(x-1)^{2}dx
derivative of \sqrt[3]{5+6x^6}	derivative\:\sqrt[3]{5+6x^{6}}
(\partial)/(\partial x)(5-x^2+xy-2^2)	\frac{\partial\:}{\partial\:x}(5-x^{2}+xy-2^{2})
derivative of (x^3+4^{-3})	\frac{d}{dx}((x^{3}+4)^{-3})
limit as x approaches 0+of 6-1/(x^2)	\lim\:_{x\to\:0+}(6-\frac{1}{x^{2}})
derivative of y=4x^{2/3}+6x^{1/2}-8	derivative\:y=4x^{\frac{2}{3}}+6x^{\frac{1}{2}}-8
integral of 8x+3	\int\:8x+3dx
(dr)/(dθ)+rtan(θ)=sec(θ)	\frac{dr}{dθ}+r\tan(θ)=\sec(θ)
f(x)=6sin(x)-4xcos(x)-x^2sin(x)	f(x)=6\sin(x)-4x\cos(x)-x^{2}\sin(x)
(\partial)/(\partial y)(50y+3000-100x)	\frac{\partial\:}{\partial\:y}(50y+3000-100x)
(\partial)/(\partial x)((59)/((1+x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{59}{(1+x^{2}+y^{2})})
slope of (1-x-x^2)(x-2),\at x=1	slope\:(1-x-x^{2})(x-2),\at\:x=1
(1+x^2)y^'+4xy=x,y(0)=1	(1+x^{2})y^{\prime\:}+4xy=x,y(0)=1
integral of 2/((1-2x)^2)	\int\:\frac{2}{(1-2x)^{2}}dx
integral from-1 to 0 of e^{-x}	\int\:_{-1}^{0}e^{-x}dx
derivative of 5tan(3x)	\frac{d}{dx}(5\tan(3x))
area 1, 1/x ,1,2	area\:1,\frac{1}{x},1,2
derivative of tan({g}(x)x)	\frac{d}{dx}(\tan({g}(x))x)
limit as x approaches 0-of x	\lim\:_{x\to\:0-}(x)
(dy)/(dx)=-y-3	\frac{dy}{dx}=-y-3
area y=6x^2,y^2= 1/6 x	area\:y=6x^{2},y^{2}=\frac{1}{6}x
y^{''}+4y=-4sin(2t)	y^{\prime\:\prime\:}+4y=-4\sin(2t)
integral of (2x)/(x^2+4)	\int\:\frac{2x}{x^{2}+4}dx
derivative of sin((pix^3))	\frac{d}{dx}(\sin((πx)^{3}))
derivative of (2x+1)^4	derivative\:(2x+1)^{4}
limit as x approaches infinity of log_{2}(((x+2))/((2*x+1)))	\lim\:_{x\to\:\infty\:}(\log_{2}(\frac{(x+2)}{(2\cdot\:x+1)}))
integral from 1 to 8 of sqrt(x-1)	\int\:_{1}^{8}\sqrt{x-1}dx
tangent of x^2sqrt(x^3+1)	tangent\:x^{2}\sqrt{x^{3}+1}
integral of (sec^2(θ))/(tan(θ))	\int\:\frac{\sec^{2}(θ)}{\tan(θ)}dθ
x^{''}-2x^'-3x=0	x^{\prime\:\prime\:}-2x^{\prime\:}-3x=0
derivative of 2sqrt(xy)	\frac{d}{dx}(2\sqrt{xy})
x^'=6(x^2+1)	x^{\prime\:}=6(x^{2}+1)
derivative of 10^{x^2}	\frac{d}{dx}(10^{x^{2}})
integral from 0 to 4 of 1/(sqrt(9+x^2))	\int\:_{0}^{4}\frac{1}{\sqrt{9+x^{2}}}dx
(\partial)/(\partial x)(-6x+12)	\frac{\partial\:}{\partial\:x}(-6x+12)
area y^2=4x,y=4x-2	area\:y^{2}=4x,y=4x-2
derivative of y= 1/(sqrt(x)),x=a	derivative\:y=\frac{1}{\sqrt{x}},x=a
derivative of a/(y^{10)}	derivative\:\frac{a}{y^{10}}
f(x)=4x^{1/2}	f(x)=4x^{\frac{1}{2}}
integral from 0 to 12 of xe^{-x}	\int\:_{0}^{12}xe^{-x}dx
derivative of y=e^{3x}cos(2x)	derivative\:y=e^{3x}\cos(2x)
derivative of 7/(x^2+3)	derivative\:\frac{7}{x^{2}+3}
integral from-1 to 1 of e^y-y^2-6	\int\:_{-1}^{1}e^{y}-y^{2}-6dy
integral of cos^4(u)	\int\:\cos^{4}(u)du
integral of sin^5(t)	\int\:\sin^{5}(t)dt
integral of (x^{20}-5x^4)^6(x^{19}-x^3)	\int\:(x^{20}-5x^{4})^{6}(x^{19}-x^{3})dx
integral of ((x^2+1))/((x+1)^2)e^x	\int\:\frac{(x^{2}+1)}{(x+1)^{2}}e^{x}dx
tangent of f(x)=x^2+5x-3,\at x=-3	tangent\:f(x)=x^{2}+5x-3,\at\:x=-3
(\partial)/(\partial y)(e^{1+x^2-y^2})	\frac{\partial\:}{\partial\:y}(e^{1+x^{2}-y^{2}})
derivative of 3/(x^4+2)	\frac{d}{dx}(\frac{3}{x^{4}+2})
integral from 0 to 2 of 6x^2-18x+12	\int\:_{0}^{2}6x^{2}-18x+12dx
tangent of f(x)=x^2-1/x ,(2,3.5)	tangent\:f(x)=x^{2}-\frac{1}{x},(2,3.5)
sum from n=1 to infinity}(((-7)^{n-1 of))/(8^n)	\sum\:_{n=1}^{\infty\:}\frac{((-7)^{n-1})}{8^{n}}
y^{''}-14y^'+49y=t^{-2}e^{7t}	y^{\prime\:\prime\:}-14y^{\prime\:}+49y=t^{-2}e^{7t}
limit as x approaches-infinity of 7/x-4	\lim\:_{x\to\:-\infty\:}(\frac{7}{x}-4)
integral of 1/(w^3)	\int\:\frac{1}{w^{3}}dw
derivative of 12sqrt(x)+16x^{3/4}	derivative\:12\sqrt{x}+16x^{\frac{3}{4}}
area f(x)=x^2-4,(-2,3)	area\:f(x)=x^{2}-4,(-2,3)
limit as x approaches 1 of x(x-1)^{-1}	\lim\:_{x\to\:1}(x(x-1)^{-1})
derivative of in	\frac{d}{dx}(in)
y^{''}+ay^'=0	y^{\prime\:\prime\:}+ay^{\prime\:}=0
integral of 12cos(3x)	\int\:12\cos(3x)dx
integral of 1+sec(x)	\int\:1+\sec(x)dx
integral of (x-y^3+y^2sin(x))	\int\:(x-y^{3}+y^{2}\sin(x))dx
integral of 1/(sqrt(-x^2+2x+15))	\int\:\frac{1}{\sqrt{-x^{2}+2x+15}}dx
inverse oflaplace 6/s+(32)/(s^2+16)	inverselaplace\:\frac{6}{s}+\frac{32}{s^{2}+16}
inverse oflaplace 8/((s^2+1)^2)	inverselaplace\:\frac{8}{(s^{2}+1)^{2}}
x^2(dy)/(dx)-y^2=0	x^{2}\frac{dy}{dx}-y^{2}=0
limit as x approaches 0 of x(ln(x))^2	\lim\:_{x\to\:0}(x(\ln(x))^{2})
integral of 4/(2x+1)	\int\:\frac{4}{2x+1}dx
tangent of 3x^4+2e^x,\at x=0	tangent\:3x^{4}+2e^{x},\at\:x=0
(x^2e^{-x})^'	(x^{2}e^{-x})^{\prime\:}

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