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

The derivative of 5ln(x+cos(x)) is 5/x-sin(x)

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

The first derivative of 5ln(x+cos(x)) is 5/x-sin(x)

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

\frac{5}{x} - sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 ln (x)) + \frac{d}{d x} (cos (x))

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

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

= \frac{5}{x} - sin (x)

What is the derivative of 5ln(x+cos(x)) ?
The derivative of 5ln(x+cos(x)) is 5/x-sin(x)
What is the first derivative of 5ln(x+cos(x)) ?
The first derivative of 5ln(x+cos(x)) is 5/x-sin(x)