What is the derivative of ln(x-sin(x)) ?

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

What is the first derivative of ln(x-sin(x)) ?

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

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\frac{d}{d x} (ln (x) - sin (x))

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

Solution steps

\frac{d}{d x} (ln (x) - sin (x))

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{x ^{3} + 6 x}{3}

g (x) = 3 x - 2 + \frac{1}{x} - \frac{1}{x ^{2}}

\int \frac{x}{2 - x - x ^{2}} d x

x y^{2} \frac{d y}{d x} = y^{3} + x^{3}

\frac{1}{s ( s ^{2} + 5 )}

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