What is the first derivative of x^2n ?

The first derivative of x^2n is 2nx

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derivative of x^2n

\frac{d}{d x} (x^{2} n)

2 n x

Solution steps

\frac{d}{d x} (x^{2} n)

Take the constant out:

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

= n \frac{d}{d x} (x^{2})

Apply the Power Rule:

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

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

Simplify

= 2 n x

f (x) = 5 + 5 x^{2} - 2 x^{3}, at x = 1

n = 0 \sum \infty \frac{7}{4 ^{n}}

y = (6 x + 5) (x^{2} - 3 x)

\int 8 x cos (4) x^{2} d x