What is the derivative of ln(e^{5x}) ?

The derivative of ln(e^{5x}) is 5

What is the first derivative of ln(e^{5x}) ?

The first derivative of ln(e^{5x}) is 5

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\frac{d}{d x} (ln (e^{5 x}))

5

Solution steps

\frac{d}{d x} (ln (e^{5 x}))

Simplify

ln (e^{5 x}) : 5 x

= \frac{d}{d x} (5 x)

Take the constant out:

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

= 5 \frac{d x}{d x}

Apply the common derivative:

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

= 5 \cdot 1

Simplify

= 5

What is the derivative of ln(e^{5x}) ?
The derivative of ln(e^{5x}) is 5
What is the first derivative of ln(e^{5x}) ?
The first derivative of ln(e^{5x}) is 5