What is the derivative of 4x^5 ?

The derivative of 4x^5 is 20x^4

What is the first derivative of 4x^5 ?

The first derivative of 4x^5 is 20x^4

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\frac{d}{d x} (4 x^{5})

20 x^{4}

Solution steps

\frac{d}{d x} (4 x^{5})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{5})

Apply the Power Rule:

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

= 4 \cdot 5 x^{5 - 1}

Simplify

= 20 x^{4}