What is the first derivative of ax^2 ?

The first derivative of ax^2 is 2ax

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derivative of ax^2

derivative of

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

\int_{- \infty}^{4} r e^{\frac{r}{2}} d r

\frac{d}{d x} (x^{2} + 5 x - 2)

\int - cos (2 θ) d θ

\frac{d y}{d x} = (x + y)^{2} + 1

\int - x^{2} + 4 d x