What is the derivative of-5x^4 ?

The derivative of-5x^4 is -20x^3

What is the first derivative of-5x^4 ?

The first derivative of-5x^4 is -20x^3

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

- 20 x^{3}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= - 20 x^{3}