What is the derivative of (5-2x^{-2}) ?

The derivative of (5-2x^{-2}) is 4/((5-2x)^3)

What is the first derivative of (5-2x^{-2}) ?

The first derivative of (5-2x^{-2}) is 4/((5-2x)^3)

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\frac{d}{d x} ((5 - 2 x)^{- 2})

\frac{4}{( 5 - 2 x ) ^{3}}

Solution steps

\frac{d}{d x} ((5 - 2 x)^{- 2})

Apply the chain rule:

- \frac{2}{( 5 - 2 x ) ^{3}} \frac{d}{d x} (5 - 2 x)

= - \frac{2}{( 5 - 2 x ) ^{3}} \frac{d}{d x} (5 - 2 x)

\frac{d}{d x} (5 - 2 x) = - 2

= - \frac{2}{( 5 - 2 x ) ^{3}} (- 2)

Simplify

- \frac{2}{( 5 - 2 x ) ^{3}} (- 2) : \frac{4}{( 5 - 2 x ) ^{3}}

= \frac{4}{( 5 - 2 x ) ^{3}}

What is the derivative of (5-2x^{-2}) ?
The derivative of (5-2x^{-2}) is 4/((5-2x)^3)
What is the first derivative of (5-2x^{-2}) ?
The first derivative of (5-2x^{-2}) is 4/((5-2x)^3)