What is the derivative of ((e^x)/(1+x^2)) ?

The derivative of ((e^x)/(1+x^2)) is (e^x(1+x^2)-2xe^x)/((1+x^2)^2)

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

\int 10 e^{x} d x

n = 1 \sum \infty ln (n)

x \to b lim (7 (- 7))

\frac{d x}{d t} = \frac{1}{x e ^{t + 2 x}}

a \to 0 lim (ln (a))

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