What is the first derivative of-x^5 ?

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

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derivative of-x^5

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

- 5 x^{4}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= - 5 x^{5 - 1}

Simplify

= - 5 x^{4}

\int (1 + x^{3})^{5} x^{2} d x

\frac{d}{d y} (x y)

x^{2} y^{^{'}} + 4 x y = \frac{sin ( 3 x )}{x ^{2}}

\int \frac{2 x - 1}{x - 1} d x

\int \frac{1}{t ^{2} 9 - t ^{2}} d t