What is the derivative of ln(e^{4x+1}) ?

The derivative of ln(e^{4x+1}) is 4

What is the first derivative of ln(e^{4x+1}) ?

The first derivative of ln(e^{4x+1}) is 4

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\frac{d}{d x} (ln (e^{4 x + 1}))

4

Solution steps

\frac{d}{d x} (ln (e^{4 x + 1}))

Simplify

ln (e^{4 x + 1}) : 4 x + 1

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= 4 + 0

Simplify

= 4

What is the derivative of ln(e^{4x+1}) ?
The derivative of ln(e^{4x+1}) is 4
What is the first derivative of ln(e^{4x+1}) ?
The first derivative of ln(e^{4x+1}) is 4