What is the derivative of 9ln(4x) ?

The derivative of 9ln(4x) is 9/x

What is the first derivative of 9ln(4x) ?

The first derivative of 9ln(4x) is 9/x

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\frac{d}{d x} (9 ln (4 x))

\frac{9}{x}

Solution steps

\frac{d}{d x} (9 ln (4 x))

Take the constant out:

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

= 9 \frac{d}{d x} (ln (4 x))

Apply the chain rule:

\frac{1}{4 x} \frac{d}{d x} (4 x)

= \frac{1}{4 x} \frac{d}{d x} (4 x)

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

= 9 \cdot \frac{1}{4 x} \cdot 4

Simplify

9 \cdot \frac{1}{4 x} \cdot 4 : \frac{9}{x}

= \frac{9}{x}

What is the derivative of 9ln(4x) ?
The derivative of 9ln(4x) is 9/x
What is the first derivative of 9ln(4x) ?
The first derivative of 9ln(4x) is 9/x