What is the derivative of f(x)=(2/3 x)^3 ?

The derivative of f(x)=(2/3 x)^3 is (8x^2)/9

What is the first derivative of f(x)=(2/3 x)^3 ?

The first derivative of f(x)=(2/3 x)^3 is (8x^2)/9

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derivative of

f (x) = (\frac{2}{3} x)^{3}

\frac{8 x ^{2}}{9}

Solution steps

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

Apply the chain rule:

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

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

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

= 3 (\frac{2}{3} x)^{2} \frac{2}{3}

Simplify

3 (\frac{2}{3} x)^{2} \frac{2}{3} : \frac{8 x ^{2}}{9}

= \frac{8 x ^{2}}{9}

What is the derivative of f(x)=(2/3 x)^3 ?
The derivative of f(x)=(2/3 x)^3 is (8x^2)/9
What is the first derivative of f(x)=(2/3 x)^3 ?
The first derivative of f(x)=(2/3 x)^3 is (8x^2)/9