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Popular >

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

Solution

derivative of

\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}}

Graph

Popular Examples

limit as x approaches h of x+h

x \to h lim (x + h)

derivative of 6/(x^2+2)

\frac{d}{d x} (\frac{6}{x ^{2} + 2})

integral from 1 to 7 of x^2

\int_{1}^{7} x^{2} d x

integral of arctanh(x)

\int arctanh (x) d x

(dy)/(dx)=(cos(x))/(sin(y))

\frac{d y}{d x} = \frac{cos ( x )}{sin ( y )}

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)