What is the derivative of ln(x-1+cos(x-1)) ?

The derivative of ln(x-1+cos(x-1)) is 1/(x-1)-sin(x-1)

What is the first derivative of ln(x-1+cos(x-1)) ?

The first derivative of ln(x-1+cos(x-1)) is 1/(x-1)-sin(x-1)

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\frac{d}{d x} (ln (x - 1) + cos (x - 1))

\frac{1}{x - 1} - sin (x - 1)

Solution steps

\frac{d}{d x} (ln (x - 1) + cos (x - 1))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x - 1)) + \frac{d}{d x} (cos (x - 1))

\frac{d}{d x} (ln (x - 1)) = \frac{1}{x - 1}

\frac{d}{d x} (cos (x - 1)) = - sin (x - 1)

= \frac{1}{x - 1} - sin (x - 1)

What is the derivative of ln(x-1+cos(x-1)) ?
The derivative of ln(x-1+cos(x-1)) is 1/(x-1)-sin(x-1)
What is the first derivative of ln(x-1+cos(x-1)) ?
The first derivative of ln(x-1+cos(x-1)) is 1/(x-1)-sin(x-1)