What is the derivative of q(x)=(8x-6)^{-1/4} ?

The derivative of q(x)=(8x-6)^{-1/4} is -2/((8x-6)^{5/4)}

What is the first derivative of q(x)=(8x-6)^{-1/4} ?

The first derivative of q(x)=(8x-6)^{-1/4} is -2/((8x-6)^{5/4)}

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derivative of

q (x) = (8 x - 6)^{- \frac{1}{4}}

- \frac{2}{( 8 x - 6 ) ^{\frac{5}{4}}}

Solution steps

\frac{d}{d x} ((8 x - 6)^{- \frac{1}{4}})

Apply the chain rule:

- \frac{1}{4 ( 8 x - 6 ) ^{\frac{5}{4}}} \frac{d}{d x} (8 x - 6)

= - \frac{1}{4 ( 8 x - 6 ) ^{\frac{5}{4}}} \frac{d}{d x} (8 x - 6)

\frac{d}{d x} (8 x - 6) = 8

= - \frac{1}{4 ( 8 x - 6 ) ^{\frac{5}{4}}} \cdot 8

Simplify

- \frac{1}{4 ( 8 x - 6 ) ^{\frac{5}{4}}} \cdot 8 : - \frac{2}{( 8 x - 6 ) ^{\frac{5}{4}}}

= - \frac{2}{( 8 x - 6 ) ^{\frac{5}{4}}}

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What is the derivative of q(x)=(8x-6)^{-1/4} ?
The derivative of q(x)=(8x-6)^{-1/4} is -2/((8x-6)^{5/4)}
What is the first derivative of q(x)=(8x-6)^{-1/4} ?
The first derivative of q(x)=(8x-6)^{-1/4} is -2/((8x-6)^{5/4)}