What is the derivative of (5x^9+7x^2-65)^{-9} ?

The derivative of (5x^9+7x^2-65)^{-9} is -(9(45x^8+14x))/((5x^9+7x^2-65)^{10)}

What is the first derivative of (5x^9+7x^2-65)^{-9} ?

The first derivative of (5x^9+7x^2-65)^{-9} is -(9(45x^8+14x))/((5x^9+7x^2-65)^{10)}

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derivative of

(5 x^{9} + 7 x^{2} - 65)^{- 9}

- \frac{9 ( 45 x ^{8} + 14 x )}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}}

Solution steps

\frac{d}{d x} ((5 x^{9} + 7 x^{2} - 65)^{- 9})

Apply the chain rule:

- \frac{9}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}} \frac{d}{d x} (5 x^{9} + 7 x^{2} - 65)

= - \frac{9}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}} \frac{d}{d x} (5 x^{9} + 7 x^{2} - 65)

\frac{d}{d x} (5 x^{9} + 7 x^{2} - 65) = 45 x^{8} + 14 x

= - \frac{9}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}} (45 x^{8} + 14 x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{9 ( 45 x ^{8} + 14 x )}{( 5 x ^{9} + 7 x ^{2} - 65 ) ^{10}}

What is the derivative of (5x^9+7x^2-65)^{-9} ?
The derivative of (5x^9+7x^2-65)^{-9} is -(9(45x^8+14x))/((5x^9+7x^2-65)^{10)}
What is the first derivative of (5x^9+7x^2-65)^{-9} ?
The first derivative of (5x^9+7x^2-65)^{-9} is -(9(45x^8+14x))/((5x^9+7x^2-65)^{10)}