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

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

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derivative of (2x^2)

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

8 x

Solution steps

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

Simplify

(2 x)^{2} : 4 x^{2}

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 8 x

f (x) = e^{2 x}

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

\frac{d}{d x} (ln (3 x^{2} + 1) ln (2 x^{3} + 1))

\int \frac{x ^{5} + x + 1}{x ^{3} - 8} d x

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