What is the derivative of sqrt(x^6) ?

The derivative of sqrt(x^6) is 3x^2

What is the first derivative of sqrt(x^6) ?

The first derivative of sqrt(x^6) is 3x^2

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\frac{d}{d x} (x^{6})

3 x^{2}

Solution steps

\frac{d}{d x} (x^{6})

Apply radical rule:

= \frac{d}{d x} (x^{\frac{6}{2}})

Apply the Power Rule:

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

= \frac{6}{2} x^{\frac{6}{2} - 1}

Simplify

= 3 x^{2}

What is the derivative of sqrt(x^6) ?
The derivative of sqrt(x^6) is 3x^2
What is the first derivative of sqrt(x^6) ?
The first derivative of sqrt(x^6) is 3x^2