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Popular Calculus Problems

tangent of f(x)= 5/(sqrt(x)),\at x= 1/4	tangent\:f(x)=\frac{5}{\sqrt{x}},\at\:x=\frac{1}{4}
integral of (y-x)	\int\:(y-x)dx
limit as x approaches-1 of (x^2-1)/(x-1)	\lim\:_{x\to\:-1}(\frac{x^{2}-1}{x-1})
integral of (2v^3-v)/(v^4-v^2)	\int\:\frac{2v^{3}-v}{v^{4}-v^{2}}dv
xy^2(dy)/(dx)=y^3-x^2	xy^{2}\frac{dy}{dx}=y^{3}-x^{2}
integral of ((e^{2x}))/(49+e^{4x)}	\int\:\frac{(e^{2x})}{49+e^{4x}}dx
(d^2)/(dx^2)(x^{6/7}+5x)	\frac{d^{2}}{dx^{2}}(x^{\frac{6}{7}}+5x)
y^'=1+ay	y^{\prime\:}=1+ay
derivative of cos(5x^2-7x(10x-7))	\frac{d}{dx}(\cos(5x^{2}-7x)(10x-7))
xy^'-3y=x^3	xy^{\prime\:}-3y=x^{3}
integral of (-4x^{3/2}+3x^{2/3}-4x^2)	\int\:(-4x^{\frac{3}{2}}+3x^{\frac{2}{3}}-4x^{2})dx
(\partial)/(\partial z)(sin(y))	\frac{\partial\:}{\partial\:z}(\sin(y))
(dy)/(dx)=((y+x))/((y-x)),y(0)=1	\frac{dy}{dx}=\frac{(y+x)}{(y-x)},y(0)=1
integral of (10X)/(X^4-13X^2+36)	\int\:\frac{10X}{X^{4}-13X^{2}+36}dX
derivative of x^{8/x}	derivative\:x^{\frac{8}{x}}
derivative of 28+(12.4)t-(0.045)t^3	derivative\:28+(12.4)t-(0.045)t^{3}
(\partial)/(\partial θ)(r(θ)cos(θ))	\frac{\partial\:}{\partial\:θ}(r(θ)\cos(θ))
integral of sin(9pi)t	\int\:\sin(9π)tdt
(\partial)/(\partial x)((4x-2y)/(4x+2y))	\frac{\partial\:}{\partial\:x}(\frac{4x-2y}{4x+2y})
integral of 1/((x+2)^{3/2)}	\int\:\frac{1}{(x+2)^{\frac{3}{2}}}dx
limit as x approaches 5 of x^2+4	\lim\:_{x\to\:5}(x^{2}+4)
integral of 3/(xsqrt(4x^2-9))	\int\:\frac{3}{x\sqrt{4x^{2}-9}}dx
integral from 0 to pi of (sin(x))/x	\int\:_{0}^{π}\frac{\sin(x)}{x}dx
derivative of f(x)=sqrt(1-6x)	derivative\:f(x)=\sqrt{1-6x}
limit as x approaches 3-of (3x+4)/(x-3)	\lim\:_{x\to\:3-}(\frac{3x+4}{x-3})
integral of sec^7(5x)tan(5x)	\int\:\sec^{7}(5x)\tan(5x)dx
integral of 3x-7	\int\:3x-7dx
tangent of f(x)=sin(x)+cos(x),\at x=0	tangent\:f(x)=\sin(x)+\cos(x),\at\:x=0
derivative of 1-x+ln(x)	\frac{d}{dx}(1-x+\ln(x))
derivative of \sqrt[7]{x^6}	derivative\:\sqrt[7]{x^{6}}
integral from 0 to a of e^{x/a}-e^{-x/a}	\int\:_{0}^{a}e^{\frac{x}{a}}-e^{-\frac{x}{a}}dx
derivative of x=6.4sin(1.2^2t^2)	derivative\:x=6.4\sin(1.2^{2}t^{2})
derivative of ln(x/5)	\frac{d}{dx}(\ln(\frac{x}{5}))
integral of 10xln(x+2)	\int\:10x\ln(x+2)dx
(\partial ^2)/(\partial x\partial y)(x^5+x^2y+x+3)	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(x^{5}+x^{2}y+x+3)
derivative of-7	derivative\:-7
y^{''}-0.2y^'+0.01y=0,y(0)=10,y^'(0)=b	y^{\prime\:\prime\:}-0.2y^{\prime\:}+0.01y=0,y(0)=10,y^{\prime\:}(0)=b
integral of cos(30x)cos(4x)cos(4x)	\int\:\cos(30x)\cdot\:\cos(4x)\cdot\:\cos(4x)dx
y^'=x+y,y(0)=10	y^{\prime\:}=x+y,y(0)=10
(\partial)/(\partial v)({u}(v,w)+ve^w)	\frac{\partial\:}{\partial\:v}({u}(v,w)+ve^{w})
sum from n=2 to infinity of 8/(nln(n))	\sum\:_{n=2}^{\infty\:}\frac{8}{n\ln(n)}
(dy)/(dx)=(e^{2x-y})/(e^{x+y)}	\frac{dy}{dx}=\frac{e^{2x-y}}{e^{x+y}}
integral of 1/(1-2x)-cos(x/3)	\int\:\frac{1}{1-2x}-\cos(\frac{x}{3})dx
(\partial)/(\partial x)(yze^x)	\frac{\partial\:}{\partial\:x}(yze^{x})
maclaurin 1/(\sqrt[3]{x^2+8)}	maclaurin\:\frac{1}{\sqrt[3]{x^{2}+8}}
y^{''}-y^'-2y=-4t+6t^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-4t+6t^{2}
integral of xe^6	\int\:xe^{6}dx
area \sqrt[3]{x}, 1/x ,[1,8]	area\:\sqrt[3]{x},\frac{1}{x},[1,8]
derivative of f(x)=-2x+3	derivative\:f(x)=-2x+3
integral of (x*cos(x))	\int\:(x\cdot\:\cos(x))dx
integral of x^2sec^2(x^3+1)	\int\:x^{2}\sec^{2}(x^{3}+1)dx
integral from 0 to 4 of 1/(u^2-16)	\int\:_{0}^{4}\frac{1}{u^{2}-16}du
sum from n=1 to infinity of 1/(n+n^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n+n^{2}}
(\partial)/(\partial x)(6x^8y^6+2x^7y^4)	\frac{\partial\:}{\partial\:x}(6x^{8}y^{6}+2x^{7}y^{4})
derivative of f(x)=-tan(x)-5cot(x)	derivative\:f(x)=-\tan(x)-5\cot(x)
derivative of x(x-1^3)	\frac{d}{dx}(x(x-1)^{3})
integral of-x^2(x+1)^3(x-1)	\int\:-x^{2}(x+1)^{3}(x-1)dx
(\partial)/(\partial y)(x^2+2y^2)	\frac{\partial\:}{\partial\:y}(x^{2}+2y^{2})
derivative of arctan((1-x/(1+x)))	\frac{d}{dx}(\arctan(\frac{1-x}{1+x}))
integral from 0 to 3 of (-x^2+x-1)	\int\:_{0}^{3}(-x^{2}+x-1)dx
integral from 1 to 16 of 1/(sqrt(x))	\int\:_{1}^{16}\frac{1}{\sqrt{x}}dx
integral of (2x)/(3(x^2+1))	\int\:\frac{2x}{3(x^{2}+1)}dx
derivative of x^{12}ln(x)	\frac{d}{dx}(x^{12}\ln(x))
integral of (16)/(x(x^2+4)^2)	\int\:\frac{16}{x(x^{2}+4)^{2}}dx
derivative of (xsin(2x)^{3/2})	\frac{d}{dx}((x\sin(2x))^{\frac{3}{2}})
integral of ((x+16))/((x^2+2x-8))	\int\:\frac{(x+16)}{(x^{2}+2x-8)}dx
(\partial)/(\partial α)({K}(α)(α)^αL^{1-α})	\frac{\partial\:}{\partial\:α}({K}(α)(α)^{α}L^{1-α})
tangent of y=11x^2,(-2,44)	tangent\:y=11x^{2},(-2,44)
integral of 1/(r(2-r^2))	\int\:\frac{1}{r(2-r^{2})}dr
limit as x approaches 1 of (3x)/(x^2-1)	\lim\:_{x\to\:1}(\frac{3x}{x^{2}-1})
taylor e^{-5x}	taylor\:e^{-5x}
integral from 1 to 9 of 1/(2x)	\int\:_{1}^{9}\frac{1}{2x}dx
derivative of 7(2xe^x+e^xx^2)	\frac{d}{dx}(7(2xe^{x}+e^{x}x^{2}))
integral of y+xe^y	\int\:y+xe^{y}dy
limit as x approaches infinity of 1*x	\lim\:_{x\to\:\infty\:}(1\cdot\:x)
derivative of (x^3-8/(x^3+8))	\frac{d}{dx}(\frac{x^{3}-8}{x^{3}+8})
(\partial)/(\partial x)(x^2y-y^2-7)	\frac{\partial\:}{\partial\:x}(x^{2}y-y^{2}-7)
integral of sec^5(4x)tan(4x)	\int\:\sec^{5}(4x)\tan(4x)dx
limit as x approaches-1 of 10x	\lim\:_{x\to\:-1}(10x)
implicit xy+5e^y=5e	implicit\:xy+5e^{y}=5e
derivative of tan(ax+b)	\frac{d}{dx}(\tan(ax+b))
(\partial)/(\partial x)(3y^2x-y^3-x^4)	\frac{\partial\:}{\partial\:x}(3y^{2}x-y^{3}-x^{4})
x^2y^{''}=y^'+(y^')^2	x^{2}y^{\prime\:\prime\:}=y^{\prime\:}+(y^{\prime\:})^{2}
(\partial)/(\partial x)(x^{xy})	\frac{\partial\:}{\partial\:x}(x^{xy})
integral of 1/(x^4-16)	\int\:\frac{1}{x^{4}-16}dx
integral from 0 to 1 of 5e^{5sqrt(x)}	\int\:_{0}^{1}5e^{5\sqrt{x}}dx
derivative of (9x/(sqrt(x)))	\frac{d}{dx}(\frac{9x}{\sqrt{x}})
limit as x approaches 0+of x^{x^8}	\lim\:_{x\to\:0+}(x^{x^{8}})
integral of 36x^3(3x^4+3)^5	\int\:36x^{3}(3x^{4}+3)^{5}dx
limit as y approaches 0 of 0/y	\lim\:_{y\to\:0}(\frac{0}{y})
tangent of f(x)=(x^2-3)(x^3-2x),\at x=-2	tangent\:f(x)=(x^{2}-3)(x^{3}-2x),\at\:x=-2
(\partial)/(\partial x)(xe^y+x^2cos(y))	\frac{\partial\:}{\partial\:x}(xe^{y}+x^{2}\cos(y))
integral of e^{1.25x}	\int\:e^{1.25x}dx
derivative of (21x^2+6x-6)/(2xsqrt(x))	derivative\:\frac{21x^{2}+6x-6}{2x\sqrt{x}}
integral of 1/(sqrt(9x^2-25))	\int\:\frac{1}{\sqrt{9x^{2}-25}}dx
integral of 1/(sqrt(x+1)+\sqrt{x-1)}	\int\:\frac{1}{\sqrt{x+1}+\sqrt{x-1}}dx
area f(x)=x^2-1,g(x)=-x+2,0,1	area\:f(x)=x^{2}-1,g(x)=-x+2,0,1
integral of (2-x)3^{(2-x)^2}	\int\:(2-x)3^{(2-x)^{2}}dx
integral from 0 to 3 of 1/(sqrt(9-x^2))	\int\:_{0}^{3}\frac{1}{\sqrt{9-x^{2}}}dx
derivative of-AB^{-x}+C	\frac{d}{dx}(-AB^{-x}+C)

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