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

The derivative of 5/((2x-3^4)) is -(40)/((2x-3)^5)

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

The first derivative of 5/((2x-3^4)) is -(40)/((2x-3)^5)

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

- \frac{40}{( 2 x - 3 ) ^{5}}

Solution steps

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

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{( 2 x - 3 ) ^{4}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

5 (- \frac{4}{( 2 x - 3 ) ^{5}} \cdot 2) : - \frac{40}{( 2 x - 3 ) ^{5}}

= - \frac{40}{( 2 x - 3 ) ^{5}}

What is the derivative of 5/((2x-3^4)) ?
The derivative of 5/((2x-3^4)) is -(40)/((2x-3)^5)
What is the first derivative of 5/((2x-3^4)) ?
The first derivative of 5/((2x-3^4)) is -(40)/((2x-3)^5)