What is the derivative of ln(e^{9x}) ?

The derivative of ln(e^{9x}) is 9

What is the first derivative of ln(e^{9x}) ?

The first derivative of ln(e^{9x}) is 9

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

9

Solution steps

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

Simplify

ln (e^{9 x}) : 9 x

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

Take the constant out:

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

= 9 \frac{d x}{d x}

Apply the common derivative:

\frac{d x}{d x} = 1

= 9 \cdot 1

Simplify

= 9

What is the derivative of ln(e^{9x}) ?
The derivative of ln(e^{9x}) is 9
What is the first derivative of ln(e^{9x}) ?
The first derivative of ln(e^{9x}) is 9