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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{2 x ^{3}}{x ^{4} + 5} d x

a cos^{2} (x) + b x

\int (sin (x) - 4 cos (x)) d x

\int \frac{x + 3}{( x - 1 ) ( x ^{2} + 1 )} d x

\frac{d}{d x} (ln (3 x + 4))

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