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

The derivative of (f(x))^3 is 3f^2x^3

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

The first derivative of (f(x))^3 is 3f^2x^3

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derivative of

(f (x))^{3}

3 f^{2} x^{3}

Solution steps

\frac{d}{df} ((f x)^{3})

Simplify

(f x)^{3} : f^{3} x^{3}

= \frac{d}{df} (f^{3} x^{3})

Treat

x

as a constant

Take the constant out:

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

= x^{3} \frac{d}{df} (f^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x^{3} \cdot 3 f^{3 - 1}

Simplify

= 3 f^{2} x^{3}

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