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

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

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

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

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\frac{d}{d x} (ln (1 + sin (x)))

\frac{cos ( x )}{1 + sin ( x )}

Solution steps

\frac{d}{d x} (ln (1 + sin (x)))

Apply the chain rule:

\frac{1}{1 + sin ( x )} \frac{d}{d x} (1 + sin (x))

= \frac{1}{1 + sin ( x )} \frac{d}{d x} (1 + sin (x))

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

= \frac{1}{1 + sin ( x )} cos (x)

Simplify

\frac{1}{1 + sin ( x )} cos (x) : \frac{cos ( x )}{1 + sin ( x )}

= \frac{cos ( x )}{1 + sin ( x )}

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