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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - x^{2} + 6 x d x

\frac{d}{d x} (arctan (4 x^{2} - 1))

\int sin^{3} (2 θ) cot (2 θ) d θ

f (x) = 2 x^{3} - x^{2} + 2, (1, 3)

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