What is the derivative of ax^3 ?

The derivative of ax^3 is 3ax^2

What is the first derivative of ax^3 ?

The first derivative of ax^3 is 3ax^2

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

3 a x^{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 3 a x^{2}

f (x) = (2 x + 1)^{\frac{1}{2}}, at x = 2

\int \frac{x ^{4}}{x ^{4} - 1} d x

\frac{d}{d x} (\frac{4 x}{1 + x ^{3}})

g (t) = t^{2} t

\frac{d}{d x} (2^{x} (π x^{2} + cos (x)))