What is the derivative of y=ln(e^{3x}) ?

The derivative of y=ln(e^{3x}) is 3

What is the first derivative of y=ln(e^{3x}) ?

The first derivative of y=ln(e^{3x}) is 3

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derivative of

y = ln (e^{3 x})

3

Solution steps

\frac{d}{d x} (ln (e^{3 x}))

Simplify

ln (e^{3 x}) : 3 x

= \frac{d}{d x} (3 x)

Take the constant out:

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

= 3 \frac{d x}{d x}

Apply the common derivative:

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

= 3 \cdot 1

Simplify

= 3

x \to 49 lim (\frac{x ^{2}}{7} - \frac{7}{x})

\frac{\partial}{\partial y} (\frac{x + y}{2})

ln (256 sin^{2} (x))

\frac{d y}{d x} = (\frac{2 y + 7}{8 x + 9})^{2}

3 x, 27

What is the derivative of y=ln(e^{3x}) ?
The derivative of y=ln(e^{3x}) is 3
What is the first derivative of y=ln(e^{3x}) ?
The first derivative of y=ln(e^{3x}) is 3