What is the first d/(da)((3a^2)^3) ?

The first d/(da)((3a^2)^3) is 162a^5

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d/(da)((3a^2)^3)

\frac{d}{d a} ((3 a^{2})^{3})

162 a^{5}

Solution steps

\frac{d}{d a} ((3 a^{2})^{3})

Simplify

(3 a^{2})^{3} : 27 a^{6}

= \frac{d}{d a} (27 a^{6})

Take the constant out:

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

= 27 \frac{d}{d a} (a^{6})

Apply the Power Rule:

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

= 27 \cdot 6 a^{6 - 1}

Simplify

= 162 a^{5}

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x^{\frac{9}{2}} e^{x}

\frac{d}{d x} (19 x^{2} + 9)