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Popular >

derivative of (x^2/(1-x^2))

Solution

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

Solution

\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}}

Graph

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Frequently Asked Questions (FAQ)

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)