What is the derivative of f(x)=(4/5 x)^4 ?

The derivative of f(x)=(4/5 x)^4 is (1024x^3)/(625)

What is the first derivative of f(x)=(4/5 x)^4 ?

The first derivative of f(x)=(4/5 x)^4 is (1024x^3)/(625)

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derivative of

f (x) = (\frac{4}{5} x)^{4}

\frac{1024 x ^{3}}{625}

Solution steps

\frac{d}{d x} ((\frac{4}{5} x)^{4})

Apply the chain rule:

4 (\frac{4}{5} x)^{3} \frac{d}{d x} (\frac{4}{5} x)

= 4 (\frac{4}{5} x)^{3} \frac{d}{d x} (\frac{4}{5} x)

\frac{d}{d x} (\frac{4}{5} x) = \frac{4}{5}

= 4 (\frac{4}{5} x)^{3} \frac{4}{5}

Simplify

4 (\frac{4}{5} x)^{3} \frac{4}{5} : \frac{1024 x ^{3}}{625}

= \frac{1024 x ^{3}}{625}

What is the derivative of f(x)=(4/5 x)^4 ?
The derivative of f(x)=(4/5 x)^4 is (1024x^3)/(625)
What is the first derivative of f(x)=(4/5 x)^4 ?
The first derivative of f(x)=(4/5 x)^4 is (1024x^3)/(625)