What is the derivative of y=ln(5x) ?

The derivative of y=ln(5x) is 1/x

What is the first derivative of y=ln(5x) ?

The first derivative of y=ln(5x) is 1/x

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derivative

\frac{1}{x}

Solution steps

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

Apply the chain rule:

\frac{1}{5 x} \frac{d}{d x} (5 x)

= \frac{1}{5 x} \frac{d}{d x} (5 x)

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

= \frac{1}{5 x} \cdot 5

Simplify

\frac{1}{5 x} \cdot 5 : \frac{1}{x}

= \frac{1}{x}

What is the derivative of y=ln(5x) ?
The derivative of y=ln(5x) is 1/x
What is the first derivative of y=ln(5x) ?
The first derivative of y=ln(5x) is 1/x