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

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

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

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

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

4

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the common derivative:

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

= 4 \cdot 1

Simplify

= 4

\frac{d}{d y} (y cos (x - y))

y = x^{3} + 6

\frac{s}{( s + 1 ) ( s + 2 )}

\frac{2}{s ^{2} + 6 s + 13}

3 sin (2 t + 5)

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