What is the derivative of 6\sqrt[3]{1-2x} ?

The derivative of 6\sqrt[3]{1-2x} is -4/((1-2x)^{2/3)}

What is the first derivative of 6\sqrt[3]{1-2x} ?

The first derivative of 6\sqrt[3]{1-2x} is -4/((1-2x)^{2/3)}

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

Solution steps

Take the constant out:

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 - 2 x) = - 2

= 6 \cdot \frac{1}{3 ( 1 - 2 x ) ^{\frac{2}{3}}} (- 2)

Simplify

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

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

What is the derivative of 6\sqrt[3]{1-2x} ?
The derivative of 6\sqrt[3]{1-2x} is -4/((1-2x)^{2/3)}
What is the first derivative of 6\sqrt[3]{1-2x} ?
The first derivative of 6\sqrt[3]{1-2x} is -4/((1-2x)^{2/3)}