What is the derivative of-1/2 x^4 ?

The derivative of-1/2 x^4 is -2x^3

What is the first derivative of-1/2 x^4 ?

The first derivative of-1/2 x^4 is -2x^3

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\frac{d}{d x} (- \frac{1}{2} x^{4})

- 2 x^{3}

Solution steps

\frac{d}{d x} (- \frac{1}{2} x^{4})

Simplify

- \frac{1}{2} x^{4} : - \frac{x ^{4}}{2}

= \frac{d}{d x} (- \frac{x ^{4}}{2})

Take the constant out:

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

= - \frac{1}{2} \frac{d}{d x} (x^{4})

Apply the Power Rule:

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

= - \frac{1}{2} \cdot 4 x^{4 - 1}

Simplify

- \frac{1}{2} \cdot 4 x^{4 - 1} : - 2 x^{3}

= - 2 x^{3}

What is the derivative of-1/2 x^4 ?
The derivative of-1/2 x^4 is -2x^3
What is the first derivative of-1/2 x^4 ?
The first derivative of-1/2 x^4 is -2x^3