What is the derivative of f(x)=(16x)^3 ?

The derivative of f(x)=(16x)^3 is 12288x^2

What is the first derivative of f(x)=(16x)^3 ?

The first derivative of f(x)=(16x)^3 is 12288x^2

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derivative of

f (x) = (16 x)^{3}

12288 x^{2}

Solution steps

\frac{d}{d x} ((16 x)^{3})

Simplify

(16 x)^{3} : 4096 x^{3}

= \frac{d}{d x} (4096 x^{3})

Take the constant out:

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

= 4096 \frac{d}{d x} (x^{3})

Apply the Power Rule:

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

= 4096 \cdot 3 x^{3 - 1}

Simplify

= 12288 x^{2}

What is the derivative of f(x)=(16x)^3 ?
The derivative of f(x)=(16x)^3 is 12288x^2
What is the first derivative of f(x)=(16x)^3 ?
The first derivative of f(x)=(16x)^3 is 12288x^2