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Popular Calculus Problems

implicit (dy)/(dx),y^2=x	implicit\:\frac{dy}{dx},y^{2}=x
(\partial)/(\partial y)(4x^2y^2)	\frac{\partial\:}{\partial\:y}(4x^{2}y^{2})
derivative of f(x)=sqrt(6x)	derivative\:f(x)=\sqrt{6x}
cos(x)((dy)/(dx))-sin(x)y=0	\cos(x)(\frac{dy}{dx})-\sin(x)y=0
limit as x approaches 1 of 3/(x^2)	\lim\:_{x\to\:1}(\frac{3}{x^{2}})
integral of xarctan(21x)	\int\:x\arctan(21x)dx
y^'-2xy=x^3y^5	y^{\prime\:}-2xy=x^{3}y^{5}
integral of xsqrt(9-x)	\int\:x\sqrt{9-x}dx
derivative of (y^2+x^2)/(y^2-x^2)	derivative\:\frac{y^{2}+x^{2}}{y^{2}-x^{2}}
tangent of f(x)= 2/x ,\at x=1	tangent\:f(x)=\frac{2}{x},\at\:x=1
tangent of x^2-3x+3	tangent\:x^{2}-3x+3
integral of 2ye^{2z}	\int\:2ye^{2z}dz
derivative of h(g^'(x))	derivative\:h(g^{\prime\:}(x))
area y= 4/x ,y=16x,y= 1/16 x	area\:y=\frac{4}{x},y=16x,y=\frac{1}{16}x
derivative of y=3xln(x)	derivative\:y=3x\ln(x)
(\partial)/(\partial x)((2x-2y)/(2x+2y))	\frac{\partial\:}{\partial\:x}(\frac{2x-2y}{2x+2y})
tangent of f(x)= 9/x ,\at x=2	tangent\:f(x)=\frac{9}{x},\at\:x=2
integral from 1 to 5 of x^2	\int\:_{1}^{5}x^{2}dx
(d^2y)/(dx^2)+y=1+x	\frac{d^{2}y}{dx^{2}}+y=1+x
integral of (4x^3-9x^2+7x)e^{-x}	\int\:(4x^{3}-9x^{2}+7x)e^{-x}dx
derivative of 7x-2	\frac{d}{dx}(7x-2)
(x+y)^2dx+(2xy+x^2-2)dy=0,y(1)=1	(x+y)^{2}dx+(2xy+x^{2}-2)dy=0,y(1)=1
derivative of f(x)=(x+5)^{2/3}(2x^2-1)^3	derivative\:f(x)=(x+5)^{\frac{2}{3}}(2x^{2}-1)^{3}
integral of 1/(1+e^{3x)}	\int\:\frac{1}{1+e^{3x}}dx
integral of 1/C	\int\:\frac{1}{C}dC
(\partial)/(\partial x)(cos^3(x^7y^7))	\frac{\partial\:}{\partial\:x}(\cos^{3}(x^{7}y^{7}))
f(x)=(x^2)/(2^x)	f(x)=\frac{x^{2}}{2^{x}}
(\partial)/(\partial x)(x^2y+sqrt(y))	\frac{\partial\:}{\partial\:x}(x^{2}y+\sqrt{y})
derivative of f(x)=-3x^3+2x^2-4x+7	derivative\:f(x)=-3x^{3}+2x^{2}-4x+7
derivative of 2.873sec(x)	\frac{d}{dx}(2.873\sec(x))
integral of (1/(1+sin(x)))	\int\:(\frac{1}{1+\sin(x)})dx
tangent of y=(x^2-x)ln(6x),\at x=2	tangent\:y=(x^{2}-x)\ln(6x),\at\:x=2
integral of xsqrt(x)+2	\int\:x\sqrt{x}+2dx
integral of 1/((5+x^2))	\int\:\frac{1}{(5+x^{2})}dx
derivative of f(x)=(x^2+3)/(x^2)	derivative\:f(x)=\frac{x^{2}+3}{x^{2}}
derivative of y=cos^2(3x-1)	derivative\:y=\cos^{2}(3x-1)
limit as x approaches 0-of 8/(5x^{1/2)}	\lim\:_{x\to\:0-}(\frac{8}{5x^{\frac{1}{2}}})
slope of (5.4)(7.7)	slope\:(5.4)(7.7)
integral of (x^2)/((15+6x-9x^2)^{3/2)}	\int\:\frac{x^{2}}{(15+6x-9x^{2})^{\frac{3}{2}}}dx
tangent of f(x)=sqrt(x+1),\at x=0	tangent\:f(x)=\sqrt{x+1},\at\:x=0
derivative of f(x)=e^{sqrt(x)}	derivative\:f(x)=e^{\sqrt{x}}
integral of sin(4x)cos(6x)	\int\:\sin(4x)\cos(6x)dx
derivative of sqrt(3x-4)	\frac{d}{dx}(\sqrt{3x-4})
derivative of-0.01549944x^2+0.287342x	derivative\:-0.01549944x^{2}+0.287342x
derivative of (10x+8x^2/((5+8x)^2))	\frac{d}{dx}(\frac{10x+8x^{2}}{(5+8x)^{2}})
inverse oflaplace s/(s+1)	inverselaplace\:\frac{s}{s+1}
integral of 1/5-7/x	\int\:\frac{1}{5}-\frac{7}{x}dx
integral from pi/2 to infinity of 7/x	\int\:_{\frac{π}{2}}^{\infty\:}\frac{7}{x}dx
integral of 1/(2+sin(x))	\int\:\frac{1}{2+\sin(x)}dx
inverse oflaplace e^{-8s}	inverselaplace\:e^{-8s}
implicit ln(xy)=e^{(x+y)}	implicit\:\ln(xy)=e^{(x+y)}
derivative of-cos(2x0.2)	\frac{d}{dx}(-\cos(2x)0.2)
integral of-11cos(ln(x))	\int\:-11\cos(\ln(x))dx
tangent of f(x)= x/(x+1),\at x=0	tangent\:f(x)=\frac{x}{x+1},\at\:x=0
derivative of f(x)=(2x-1)(6x-6)^{-1}	derivative\:f(x)=(2x-1)(6x-6)^{-1}
derivative of f(x)=(x^2)/(x+2)	derivative\:f(x)=\frac{x^{2}}{x+2}
(tan(y))dx-(cot(x))dy=0	(\tan(y))dx-(\cot(x))dy=0
integral of (x-9)/((x+5)(x-2))	\int\:\frac{x-9}{(x+5)(x-2)}dx
(\partial)/(\partial x)(2y-x^2+2)	\frac{\partial\:}{\partial\:x}(2y-x^{2}+2)
tangent of 2e^{x-2}	tangent\:2e^{x-2}
derivative of \sqrt[3]{7x^6+8x^5}	derivative\:\sqrt[3]{7x^{6}+8x^{5}}
sin(x)sin(y)+y^'cos(y)=0	\sin(x)\sin(y)+y^{\prime\:}\cos(y)=0
derivative of 3x^2-6x+7	\frac{d}{dx}(3x^{2}-6x+7)
derivative of (sqrt(x)+1)/(x^2+1)	derivative\:\frac{\sqrt{x}+1}{x^{2}+1}
derivative of xe^{x^6}	\frac{d}{dx}(xe^{x^{6}})
derivative of 2(12)(18)+2(9)	derivative\:2(12)(18)+2(9)
(dr)/(dθ)=8cos(θ)	\frac{dr}{dθ}=8\cos(θ)
integral of 92	\int\:92
limit as t approaches 0 of ((3^t-2^t))/t	\lim\:_{t\to\:0}(\frac{(3^{t}-2^{t})}{t})
integral of ((3x-2))/(1-6x-9x^2)	\int\:\frac{(3x-2)}{1-6x-9x^{2}}dx
(\partial)/(\partial y)(((-y^2))/((x-y)^2))	\frac{\partial\:}{\partial\:y}(\frac{(-y^{2})}{(x-y)^{2}})
limit as x approaches 5-of 2/x	\lim\:_{x\to\:5-}(\frac{2}{x})
limit as x approaches 2 of (sqrt(x^2+6x)-2x)/(sqrt(x)-\sqrt{2)}	\lim\:_{x\to\:2}(\frac{\sqrt{x^{2}+6x}-2x}{\sqrt{x}-\sqrt{2}})
1/(x^5)(dy)/(dx)=2+18y	\frac{1}{x^{5}}\frac{dy}{dx}=2+18y
derivative of cos^8(x)	derivative\:\cos^{8}(x)
(\partial)/(\partial x)(5ycos(x))	\frac{\partial\:}{\partial\:x}(5y\cos(x))
integral of e^{1/2 ln(x)}	\int\:e^{\frac{1}{2}\ln(x)}dx
sum from n=1 to infinity of 1/2 (1/2)^n	\sum\:_{n=1}^{\infty\:}\frac{1}{2}(\frac{1}{2})^{n}
y^'=((e^x))/(e^y),y(0)=2	y^{\prime\:}=\frac{(e^{x})}{e^{y}},y(0)=2
sum from n=0 to infinity of 1/(n^2+9n+20)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+9n+20}
derivative of f(x)=x^2-2x+3	derivative\:f(x)=x^{2}-2x+3
tangent of y=(-8x)/(x^2+1)	tangent\:y=\frac{-8x}{x^{2}+1}
derivative of (4x)/(x+3)	derivative\:\frac{4x}{x+3}
limit as x approaches-1 of ln(5+2x)	\lim\:_{x\to\:-1}(\ln(5+2x))
limit as x approaches 0 of e^{5/x}	\lim\:_{x\to\:0}(e^{\frac{5}{x}})
(\partial)/(\partial x)(x^2+y^2+3)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+3)
integral of arccos(8x)	\int\:\arccos(8x)dx
derivative of 12x^3-6x^2	\frac{d}{dx}(12x^{3}-6x^{2})
derivative of y/(x^5)	derivative\:\frac{y}{x^{5}}
integral of 5\sqrt[4]{x}	\int\:5\sqrt[4]{x}dx
derivative of sqrt(4^2)	derivative\:\sqrt{4^{2}}
limit as x approaches-2 of-x	\lim\:_{x\to\:-2}(-x)
derivative of y/((x^2+y^2))	\frac{d}{dx}(\frac{y}{(x^{2}+y^{2})})
taylor 5^x	taylor\:5^{x}
y^'-2xy=0	y^{\prime\:}-2xy=0
(dy}{dx}=\frac{1+y)/x	\frac{dy}{dx}=\frac{1+y}{x}
integral of arccot(16y)	\int\:\arccot(16y)dy
limit as x approaches-2 of-3x	\lim\:_{x\to\:-2}(-3x)
integral of sqrt(x+3)	\int\:\sqrt{x+3}dx
(dy)/(dx)=(2sec(y))/((x-4)^2)	\frac{dy}{dx}=\frac{2\sec(y)}{(x-4)^{2}}

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