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

The derivative of f(x)= x/(1+x^2) is (1-x^2)/((1+x^2)^2)

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

The first derivative of f(x)= x/(1+x^2) is (1-x^2)/((1+x^2)^2)

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derivative

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

1 \cdot (1 + x^{2}) - 2 xx = 1 - x^{2}

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

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