What is the first derivative of-x^4 ?

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

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derivative of-x^4

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

- 4 x^{3}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= - 4 x^{4 - 1}

Simplify

= - 4 x^{3}

h \to 0 lim (\frac{( - 4 + h ) + 4}{h})

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