What is the derivative of-2x^5 ?

The derivative of-2x^5 is -10x^4

What is the first derivative of-2x^5 ?

The first derivative of-2x^5 is -10x^4

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\frac{d}{d x} (- 2 x^{5})

- 10 x^{4}

Solution steps

\frac{d}{d x} (- 2 x^{5})

Take the constant out:

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

= - 2 \frac{d}{d x} (x^{5})

Apply the Power Rule:

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

= - 2 \cdot 5 x^{5 - 1}

Simplify

= - 10 x^{4}

t e^{(- 3 t)} sin (5 t)

\frac{\partial}{\partial y} (y^{2} + x y^{3})

\frac{d}{d x} ((x - 4)^{3} + 3 x (x - 4)^{2})

\int (2 sin (4 x) - 8 cos (3 x)) d x

\int_{0}^{1} x e^{- 5 x} d x