What is the d/(dt)(ln(cos(t))) ?

The d/(dt)(ln(cos(t))) is -tan(t)

What is the first d/(dt)(ln(cos(t))) ?

The first d/(dt)(ln(cos(t))) is -tan(t)

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\frac{d}{d t} (ln (cos (t)))

- tan (t)

Solution steps

\frac{d}{d t} (ln (cos (t)))

Apply the chain rule:

\frac{1}{cos ( t )} \frac{d}{d t} (cos (t))

= \frac{1}{cos ( t )} \frac{d}{d t} (cos (t))

\frac{d}{d t} (cos (t)) = - sin (t)

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

Simplify

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

= - tan (t)

\frac{d}{d x} y^{4} = \frac{d}{d x} (4 x)

x, 11, \frac{1}{44} x^{2}

\int 2 \frac{y}{5} d y

\int \frac{x}{9 - x ^{4}} d x

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = - 1