What is (\partial)/(\partial x)(ln(cos(x))) ?

The answer to (\partial)/(\partial x)(ln(cos(x))) is -tan(x)

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(\partial)/(\partial x)(ln(cos(x)))

\frac{\partial}{\partial x} (ln (cos (x)))

- tan (x)

Solution steps

\frac{\partial}{\partial x} (ln (cos (x)))

Apply the chain rule:

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

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

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

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

Simplify

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

= - tan (x)

\frac{( x ^{2} )}{x ^{2} + 27}

\frac{d}{d x} (\frac{cos ( x )}{lo g _{3} ( x )})

\int \frac{x}{4 x ^{2} + 5} d x

\frac{\partial}{\partial x} (\frac{r x ( K ( r , x ) - x )}{K ( r , x ) + a x})

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

What is (\partial)/(\partial x)(ln(cos(x))) ?
The answer to (\partial)/(\partial x)(ln(cos(x))) is -tan(x)