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Popular Calculus Problems

tangent of y=((x+2))/((x+1)^2),\at x=0	tangent\:y=\frac{(x+2)}{(x+1)^{2}},\at\:x=0
(\partial)/(\partial x)(sin(pi(5x-y)))	\frac{\partial\:}{\partial\:x}(\sin(π(5x-y)))
y^2y^'=e^x	y^{2}y^{\prime\:}=e^{x}
limit as x approaches infinity of f(x)	\lim\:_{x\to\:\infty\:}(f(x))
derivative of 3x^2sin(x+3xcos(x))	\frac{d}{dx}(3x^{2}\sin(x)+3x\cos(x))
d/(dt)(acos(3t)+bsin(3t))	\frac{d}{dt}(a\cos(3t)+b\sin(3t))
(\partial)/(\partial a)(a/(sin(θ)))	\frac{\partial\:}{\partial\:a}(\frac{a}{\sin(θ)})
derivative of xarctan(x)	\frac{d}{dx}(x\arctan(x))
x(dy)/(dx)=y+sqrt(x^2+y^2)	x\frac{dy}{dx}=y+\sqrt{x^{2}+y^{2}}
integral of sin^3(x)x	\int\:\sin^{3}(x)xdx
limit as x approaches 1 of sqrt(1+x)	\lim\:_{x\to\:1}(\sqrt{1+x})
(d^2)/(dx^2)(8z^2e^z)	\frac{d^{2}}{dx^{2}}(8z^{2}e^{z})
derivative of f(x)=sqrt(2x+9)	derivative\:f(x)=\sqrt{2x+9}
integral of (sin(2x+1))/(cos^2(2x+1))	\int\:\frac{\sin(2x+1)}{\cos^{2}(2x+1)}dx
derivative of (2x+1^3)	\frac{d}{dx}((2x+1)^{3})
derivative of f(x)=4sqrt(x)-x	derivative\:f(x)=4\sqrt{x}-x
derivative of cos^3(x/(x+1))	\frac{d}{dx}(\cos^{3}(\frac{x}{x+1}))
limit as x approaches infinity of x-5	\lim\:_{x\to\:\infty\:}(x-5)
taylor e^{-x}0.25	taylor\:e^{-x}0.25
tangent of f(x)=1-2x^2,-7,\at x=2	tangent\:f(x)=1-2x^{2},-7,\at\:x=2
derivative of \sqrt[4]{(3x-2/(x^2+1)})	\frac{d}{dx}(\sqrt[4]{\frac{3x-2}{x^{2}+1}})
tangent of f(x)=5x-4sqrt(x),\at x=1	tangent\:f(x)=5x-4\sqrt{x},\at\:x=1
tangent of y= 1/(5+2x),(2, 1/9)	tangent\:y=\frac{1}{5+2x},(2,\frac{1}{9})
(y^'-e^{-t}+4)/y =-4,y(0)=-4	\frac{y^{\prime\:}-e^{-t}+4}{y}=-4,y(0)=-4
integral of x^3sqrt(x^2+45)	\int\:x^{3}\sqrt{x^{2}+45}dx
(2y+1)dx+((x^2-y)/x)dy=0	(2y+1)dx+(\frac{x^{2}-y}{x})dy=0
integral from 0 to 2 of (x(64-(x+3)^3))	\int\:_{0}^{2}(x(64-(x+3)^{3}))dx
derivative of (x^2-x^3)	\frac{d}{dx}((x^{2}-x)^{3})
derivative of 1/3 (x^2+2^{3/2}-5)	\frac{d}{dx}(\frac{1}{3}(x^{2}+2)^{\frac{3}{2}}-5)
derivative of 1/(sec^2(x))	\frac{d}{dx}(\frac{1}{\sec^{2}(x)})
tangent of f(x)= 2/(x+1),\at x=7	tangent\:f(x)=\frac{2}{x+1},\at\:x=7
limit as x approaches 0+of (12)/(x^2)	\lim\:_{x\to\:0+}(\frac{12}{x^{2}})
integral from 0 to 2 of (x^2)/2	\int\:_{0}^{2}\frac{x^{2}}{2}dx
integral of 3/(sqrt(4x-x^2))	\int\:\frac{3}{\sqrt{4x-x^{2}}}dx
integral of (2x^2+2)/((x^2-2x+2)^2)	\int\:\frac{2x^{2}+2}{(x^{2}-2x+2)^{2}}dx
derivative of g(x)=(6x^2)/(2-x)	derivative\:g(x)=\frac{6x^{2}}{2-x}
integral of sin^4(3x)-cos^4(3x)	\int\:\sin^{4}(3x)-\cos^{4}(3x)dx
integral of e^{-st}*sin(t)	\int\:e^{-st}\cdot\:\sin(t)dt
integral of 1/(x^{1/3)+1}	\int\:\frac{1}{x^{\frac{1}{3}}+1}dx
(dy)/(dx)=xe^{2y}	\frac{dy}{dx}=xe^{2y}
inverse oflaplace 1/((s-1)*(s-2))	inverselaplace\:\frac{1}{(s-1)\cdot\:(s-2)}
derivative of 6arcsin(x^3)	\frac{d}{dx}(6\arcsin(x^{3}))
derivative of (1+cos(2x)^2)	\frac{d}{dx}((1+\cos(2x))^{2})
derivative of (x^2-2sqrt(x)/x)	\frac{d}{dx}(\frac{x^{2}-2\sqrt{x}}{x})
tangent of f(x)=sqrt(x^2+3x),(1,2)	tangent\:f(x)=\sqrt{x^{2}+3x},(1,2)
integral of (9-9x)/(1-sqrt(x))	\int\:\frac{9-9x}{1-\sqrt{x}}dx
tangent of y=sqrt(x),\at x=4	tangent\:y=\sqrt{x},\at\:x=4
sum from n=0 to infinity} 1/(sqrt(n) of-1/(\sqrt{n+1))	\sum\:_{n=0}^{\infty\:}\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}
y^{'''}+4y^{''}+4y^'=8x	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:\prime\:}+4y^{\prime\:}=8x
integral of x^4e^{x/2}	\int\:x^{4}e^{\frac{x}{2}}dx
(\partial)/(\partial x)(sqrt(2g(x)x))	\frac{\partial\:}{\partial\:x}(\sqrt{2g(x)x})
(dy)/(dx)= x/(9y)	\frac{dy}{dx}=\frac{x}{9y}
(\partial)/(\partial x)(8arcsin(x^2))	\frac{\partial\:}{\partial\:x}(8\arcsin(x^{2}))
(dy)/(dx)=(e^x-1)/(e^y),f(1)=0	\frac{dy}{dx}=\frac{e^{x}-1}{e^{y}},f(1)=0
derivative of 7sqrt(x)	derivative\:7\sqrt{x}
derivative of (x-1^2\sqrt[3]{x+2})	\frac{d}{dx}((x-1)^{2}\sqrt[3]{x+2})
derivative of (3x^{3/5}-x)/(x-1)	derivative\:\frac{3x^{\frac{3}{5}}-x}{x-1}
integral of (x+1)/(x^2+2x+5)	\int\:\frac{x+1}{x^{2}+2x+5}dx
integral of-5x^4	\int\:-5x^{4}dx
integral of csc^2(x)-2e^x	\int\:\csc^{2}(x)-2e^{x}dx
integral from 0 to 1/4 of 1/(1+16x^2)	\int\:_{0}^{\frac{1}{4}}\frac{1}{1+16x^{2}}dx
(dy)/(dt)=y^2t^2	\frac{dy}{dt}=y^{2}t^{2}
integral of xcos(x^2+1)	\int\:x\cos(x^{2}+1)dx
y^{''}+4sqrt(6)y^'+24y=0	y^{\prime\:\prime\:}+4\sqrt{6}y^{\prime\:}+24y=0
derivative of cot(x^3)	\frac{d}{dx}(\cot(x^{3}))
limit as x approaches 0 of+(1/x)	\lim\:_{x\to\:0}(+(\frac{1}{x}))
(x^2-1)y^'+2xy^2=0	(x^{2}-1)y^{\prime\:}+2xy^{2}=0
d/(dθ)(6cos(θ)cos(θ))	\frac{d}{dθ}(6\cos(θ)\cos(θ))
sum from n=1 to infinity of 4/(n(n+1))	\sum\:_{n=1}^{\infty\:}\frac{4}{n(n+1)}
derivative of ln(x+1/(ln(x)))	\frac{d}{dx}(\ln(x)+\frac{1}{\ln(x)})
limit as x approaches 0 of sqrt(1+2x)	\lim\:_{x\to\:0}(\sqrt{1+2x})
derivative of \sqrt[3]{n/4}+50	derivative\:\sqrt[3]{\frac{n}{4}}+50
(\partial)/(\partial x)(xe^{x^2y^2})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}y^{2}})
limit as x approaches 1 of b+1/(x-1)	\lim\:_{x\to\:1}(b+\frac{1}{x-1})
area y=4x,y= 4/x ,x=4	area\:y=4x,y=\frac{4}{x},x=4
inverse oflaplace 1/(s(s^2+6s+13))	inverselaplace\:\frac{1}{s(s^{2}+6s+13)}
limit as x approaches 1 of sqrt(10x+15)	\lim\:_{x\to\:1}(\sqrt{10x+15})
integral of ((x^2)/4+2x+3)	\int\:(\frac{x^{2}}{4}+2x+3)dx
derivative of (ln(6x)/(6x))	\frac{d}{dx}(\frac{\ln(6x)}{6x})
(dy)/(dx)=sqrt(5y)*e^{x+6}	\frac{dy}{dx}=\sqrt{5y}\cdot\:e^{x+6}
derivative of (ln(x)^2(sin(x)))	\frac{d}{dx}((\ln(x))^{2}(\sin(x)))
(x^2+2xy-4y^2)dx-(x^2-8xy-4y^2)dy=0	(x^{2}+2xy-4y^{2})dx-(x^{2}-8xy-4y^{2})dy=0
derivative of y=(f(x))/(x^9)	derivative\:y=\frac{f(x)}{x^{9}}
derivative of sin(x)cos(x)-sin^2(x)+x	derivative\:\sin(x)\cos(x)-\sin^{2}(x)+x
tangent of f(x)=sqrt(x/5),\at x=125	tangent\:f(x)=\sqrt{\frac{x}{5}},\at\:x=125
integral of 3xe^{-x}	\int\:3xe^{-x}dx
integral of (y+1)^2	\int\:(y+1)^{2}dy
limit as x approaches 0 of (e^{8x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{8x}-1}{x})
slope ofintercept (2,1),(-4,-2)	slopeintercept\:(2,1),(-4,-2)
integral of 4x^2cos(x/5)	\int\:4x^{2}\cos(\frac{x}{5})dx
limit as x approaches 3-of 2/((x-3)^3)	\lim\:_{x\to\:3-}(\frac{2}{(x-3)^{3}})
integral of (sqrt(x)-5)/(sqrt(x)+3)	\int\:\frac{\sqrt{x}-5}{\sqrt{x}+3}dx
area y=(x-2)^2,y=x	area\:y=(x-2)^{2},y=x
derivative of f(x)=arcsin(3x)	derivative\:f(x)=\arcsin(3x)
derivative of f(x)=2x(x^2+1)	derivative\:f(x)=2x(x^{2}+1)
integral of 7x(x^2+2)^2	\int\:7x(x^{2}+2)^{2}dx
integral of cot(x)cos(x)	\int\:\cot(x)\cos(x)dx
integral from-2 to 2 of x(4-x^2)	\int\:_{-2}^{2}x(4-x^{2})dx
integral from 0 to pi of (sin^2(x))^2	\int\:_{0}^{π}(\sin^{2}(x))^{2}dx
4xy^'-20y=x^{-9}	4xy^{\prime\:}-20y=x^{-9}

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