What is the derivative of-3x^5 ?

The derivative of-3x^5 is -15x^4

What is the first derivative of-3x^5 ?

The first derivative of-3x^5 is -15x^4

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\frac{d}{d x} (- 3 x^{5})

- 15 x^{4}

Solution steps

\frac{d}{d x} (- 3 x^{5})

Take the constant out:

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

= - 3 \frac{d}{d x} (x^{5})

Apply the Power Rule:

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

= - 3 \cdot 5 x^{5 - 1}

Simplify

= - 15 x^{4}

\frac{d}{d y} (ln (x^{4} + y^{4}))

\frac{\partial}{\partial w} (u (v, w) + v e^{w})

\frac{x ^{3}}{3} + \frac{1}{4 x}

f (x) = \frac{2}{5 x ^{2}}

\frac{\partial}{\partial x} (\frac{( 1 + x )}{1 + y} z^{2})