What is the derivative of 5x^5 ?

The derivative of 5x^5 is 25x^4

What is the first derivative of 5x^5 ?

The first derivative of 5x^5 is 25x^4

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

25 x^{4}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 25 x^{4}

x \to 0 lim (cot (x) - csc (x))

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

\frac{d}{d x} (e^{c o t (x^{2})})

\frac{d y}{d x} = \frac{4 x y}{2 + x ^{2}}

ma c l a u r in (1 + x)^{- \frac{4}{5}}