What is the derivative of ax^4 ?

The derivative of ax^4 is 4ax^3

What is the first derivative of ax^4 ?

The first derivative of ax^4 is 4ax^3

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

4 a x^{3}

Solution steps

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

Take the constant out:

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

= a \frac{d}{d x} (x^{4})

Apply the Power Rule:

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

= a \cdot 4 x^{4 - 1}

Simplify

= 4 a x^{3}

n = 1 \sum \infty n^{2} (\frac{5}{6})^{n}

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