What is the derivative of ln({g}(x)) ?

The derivative of ln({g}(x)) is (derivative of {g}(x))/({g)(x)}

What is the first derivative of ln({g}(x)) ?

The first derivative of ln({g}(x)) is (derivative of {g}(x))/({g)(x)}

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

\frac{\frac{d}{d x} ( g ( x ) )}{g ( x )}

Solution steps

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

Apply the chain rule:

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

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

Simplify

\frac{1}{g ( x )} \frac{d}{d x} (g (x)) : \frac{\frac{d}{d x} ( g ( x ) )}{g ( x )}

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

What is the derivative of ln({g}(x)) ?
The derivative of ln({g}(x)) is (derivative of {g}(x))/({g)(x)}
What is the first derivative of ln({g}(x)) ?
The first derivative of ln({g}(x)) is (derivative of {g}(x))/({g)(x)}