What is the derivative of 2(x^4) ?

The derivative of 2(x^4) is 8x^3

What is the first derivative of 2(x^4) ?

The first derivative of 2(x^4) is 8x^3

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\frac{d}{d x} (2 (x)^{4})

8 x^{3}

Solution steps

\frac{d}{d x} (2 (x)^{4})

Take the constant out:

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

= 2 \frac{d}{d x} (x^{4})

Apply the Power Rule:

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

= 2 \cdot 4 x^{4 - 1}

Simplify

= 8 x^{3}

\frac{d}{d x} (\frac{6 x ^{2} + 4}{3 y ^{2} - 4})

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

\frac{d}{d x} (3^{2 x^{2}} \cdot x)

\frac{d}{d x} (\frac{10}{x ^{2} + 1})

x \to - 4 lim (\frac{1}{2} x - 1)