What is the derivative of ln(e^{6x}) ?

The derivative of ln(e^{6x}) is 6

What is the first derivative of ln(e^{6x}) ?

The first derivative of ln(e^{6x}) is 6

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\frac{d}{d x} (ln (e^{6 x}))

6

Solution steps

\frac{d}{d x} (ln (e^{6 x}))

Simplify

ln (e^{6 x}) : 6 x

= \frac{d}{d x} (6 x)

Take the constant out:

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

= 6 \frac{d x}{d x}

Apply the common derivative:

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

= 6 \cdot 1

Simplify

= 6

\int (\frac{1}{9 - x ^{2}}) d x

f^{^{''}} (x) = (7 + 6 x)^{e^{- 5 x}}

\int x (3 - 5 x) d x

\frac{d}{d x} (cos^{3} (e^{- x}))

\int cos (\frac{mπ x}{3}) d x

What is the derivative of ln(e^{6x}) ?
The derivative of ln(e^{6x}) is 6
What is the first derivative of ln(e^{6x}) ?
The first derivative of ln(e^{6x}) is 6