What is the derivative of f(x)=\sqrt[3]{4-9x} ?

The derivative of f(x)=\sqrt[3]{4-9x} is -3/((4-9x)^{2/3)}

What is the first derivative of f(x)=\sqrt[3]{4-9x} ?

The first derivative of f(x)=\sqrt[3]{4-9x} is -3/((4-9x)^{2/3)}

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derivative of

f (x) = 3 4 - 9 x

- \frac{3}{( 4 - 9 x ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 4 - 9 x)

Apply the chain rule:

\frac{1}{3 ( 4 - 9 x ) ^{\frac{2}{3}}} \frac{d}{d x} (4 - 9 x)

= \frac{1}{3 ( 4 - 9 x ) ^{\frac{2}{3}}} \frac{d}{d x} (4 - 9 x)

\frac{d}{d x} (4 - 9 x) = - 9

= \frac{1}{3 ( 4 - 9 x ) ^{\frac{2}{3}}} (- 9)

Simplify

\frac{1}{3 ( 4 - 9 x ) ^{\frac{2}{3}}} (- 9) : - \frac{3}{( 4 - 9 x ) ^{\frac{2}{3}}}

= - \frac{3}{( 4 - 9 x ) ^{\frac{2}{3}}}

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What is the derivative of f(x)=\sqrt[3]{4-9x} ?
The derivative of f(x)=\sqrt[3]{4-9x} is -3/((4-9x)^{2/3)}
What is the first derivative of f(x)=\sqrt[3]{4-9x} ?
The first derivative of f(x)=\sqrt[3]{4-9x} is -3/((4-9x)^{2/3)}