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Popular >

derivative of (e^x/(x^2+1))

Solution

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 1})

Solution

\frac{e ^{x} ( x ^{2} + 1 ) - 2 x e ^{x}}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{x} ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) e ^{x}}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (x^{2} + 1) = 2 x

= \frac{e ^{x} ( x ^{2} + 1 ) - 2 x e ^{x}}{( x ^{2} + 1 ) ^{2}}

Popular Examples

integral of 18x

\int 18 x d x

implicit (dy)/(dx),8x^3+x^2y-xy^3=9 implicit derivative

\frac{d y}{d x}, 8 x^{3} + x^{2} y - x y^{3} = 9

integral of 1/(x^{4/5)(1+x^{1/5})}

\int \frac{1}{x ^{\frac{4}{5}} ( 1 + x ^{\frac{1}{5}} )} d x

x((dy)/(dx))=2x^2+y

x (\frac{d y}{d x}) = 2 x^{2} + y

tangent of f(x)=sqrt(7x+32),\at x=-1 tangent of

f (x) = 7 x + 32, at x = - 1

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(x^2+1)) ?
The derivative of (e^x/(x^2+1)) is (e^x(x^2+1)-2xe^x)/((x^2+1)^2)
What is the first derivative of (e^x/(x^2+1)) ?
The first derivative of (e^x/(x^2+1)) is (e^x(x^2+1)-2xe^x)/((x^2+1)^2)