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Popular Calculus >

derivative of (3-4x^{4/3})

Solution

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

Solution

- \frac{16 ( 3 - 4 x ) ^{\frac{1}{3}}}{3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{4 ( 3 - 4 x ) ^{\frac{1}{3}}}{3} (- 4) : - \frac{16 ( 3 - 4 x ) ^{\frac{1}{3}}}{3}

= - \frac{16 ( 3 - 4 x ) ^{\frac{1}{3}}}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3-4x^{4/3}) ?
The derivative of (3-4x^{4/3}) is -(16(3-4x)^{1/3})/3
What is the first derivative of (3-4x^{4/3}) ?
The first derivative of (3-4x^{4/3}) is -(16(3-4x)^{1/3})/3