What is the derivative of ln(sqrt(4+5x)) ?

The derivative of ln(sqrt(4+5x)) is 5/(2(4+5x))

What is the first derivative of ln(sqrt(4+5x)) ?

The first derivative of ln(sqrt(4+5x)) is 5/(2(4+5x))

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\frac{d}{d x} (ln (4 + 5 x))

\frac{5}{2 ( 4 + 5 x )}

Solution steps

\frac{d}{d x} (ln (4 + 5 x))

Apply the chain rule:

\frac{1}{4 + 5 x} \frac{d}{d x} (4 + 5 x)

= \frac{1}{4 + 5 x} \frac{d}{d x} (4 + 5 x)

\frac{d}{d x} (4 + 5 x) = \frac{5}{2 4 + 5 x}

= \frac{1}{4 + 5 x} \cdot \frac{5}{2 4 + 5 x}

Simplify

\frac{1}{4 + 5 x} \cdot \frac{5}{2 4 + 5 x} : \frac{5}{2 ( 4 + 5 x )}

= \frac{5}{2 ( 4 + 5 x )}

What is the derivative of ln(sqrt(4+5x)) ?
The derivative of ln(sqrt(4+5x)) is 5/(2(4+5x))
What is the first derivative of ln(sqrt(4+5x)) ?
The first derivative of ln(sqrt(4+5x)) is 5/(2(4+5x))