What is the derivative of (4x^2) ?

The derivative of (4x^2) is 32x

What is the first derivative of (4x^2) ?

The first derivative of (4x^2) is 32x

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\frac{d}{d x} ((4 x)^{2})

32 x

Solution steps

\frac{d}{d x} ((4 x)^{2})

Simplify

(4 x)^{2} : 16 x^{2}

= \frac{d}{d x} (16 x^{2})

Take the constant out:

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

= 16 \frac{d}{d x} (x^{2})

Apply the Power Rule:

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

= 16 \cdot 2 x^{2 - 1}

Simplify

= 32 x