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Popular >

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

Solution

derivative of

f (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 (7x^2)e^{x^3+1}

\int (7 x^{2}) e^{x^{3} + 1} d x

integral of e^{-2y}y

\int e^{- 2 y} y d y

tangent of f(x)=-x^3+x^2+4x-2,\at x=0 tangent of

f (x) = - x^{3} + x^{2} + 4 x - 2, at x = 0

(\partial)/(\partial y)(ye^{xy}sin(y))

\frac{\partial}{\partial y} (y e^{x y} sin (y))

limit as x approaches 2-of 3x

x \to 2 - lim (3 x)

Frequently Asked Questions (FAQ)

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