What is the derivative of 3(1-x^{-2}) ?

The derivative of 3(1-x^{-2}) is 6/((1-x)^3)

What is the first derivative of 3(1-x^{-2}) ?

The first derivative of 3(1-x^{-2}) is 6/((1-x)^3)

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

\frac{6}{( 1 - x ) ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 - x) = - 1

= 3 (- \frac{2}{( 1 - x ) ^{3}} (- 1))

Simplify

3 (- \frac{2}{( 1 - x ) ^{3}} (- 1)) : \frac{6}{( 1 - x ) ^{3}}

= \frac{6}{( 1 - x ) ^{3}}

What is the derivative of 3(1-x^{-2}) ?
The derivative of 3(1-x^{-2}) is 6/((1-x)^3)
What is the first derivative of 3(1-x^{-2}) ?
The first derivative of 3(1-x^{-2}) is 6/((1-x)^3)