What is the derivative of ln(9x^6) ?

The derivative of ln(9x^6) is 12ln(3)x^5

What is the first derivative of ln(9x^6) ?

The first derivative of ln(9x^6) is 12ln(3)x^5

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\frac{d}{d x} (ln (9) x^{6})

12 ln (3) x^{5}

Solution steps

\frac{d}{d x} (ln (9) x^{6})

Simplify

ln (9) x^{6} : 2 ln (3) x^{6}

= \frac{d}{d x} (2 ln (3) x^{6})

Take the constant out:

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

= 2 ln (3) \frac{d}{d x} (x^{6})

Apply the Power Rule:

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

= 2 ln (3) \cdot 6 x^{6 - 1}

Simplify

= 12 ln (3) x^{5}

What is the derivative of ln(9x^6) ?
The derivative of ln(9x^6) is 12ln(3)x^5
What is the first derivative of ln(9x^6) ?
The first derivative of ln(9x^6) is 12ln(3)x^5