What is the first derivative of Ax^2 ?

The first derivative of Ax^2 is 2Ax

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derivative of Ax^2

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

2 A x

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 A x