What is the first (ln(cos(x)))^' ?

The first (ln(cos(x)))^' is -tan(x)

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(ln(cos(x)))^'

(ln (cos (x)))^{^{'}}

- tan (x)

Solution steps

(ln (cos (x)))^{'}

Apply the chain rule:

\frac{1}{cos ( x )} (cos (x))^{'}

= \frac{1}{cos ( x )} (cos (x))^{'}

(cos (x))^{'} = - sin (x)

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

Simplify

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

= - tan (x)

x \to 3 lim (\frac{x ^{2} - 5}{x - 3})

x \to 0 lim (\frac{4 tan ( x )}{x})

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

\int_{- 6}^{6} 3 x - 4 d x

y^{^{'}} = y^{2} \cdot cos (x)