What is the derivative of f(t)=ln(cos(t)) ?

The derivative of f(t)=ln(cos(t)) is -tan(t)

What is the first derivative of f(t)=ln(cos(t)) ?

The first derivative of f(t)=ln(cos(t)) is -tan(t)

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derivative of

f (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)

f (x) = e^{x} cos (x), (0, 1)

\frac{\partial}{\partial x} (ln (7 x^{2} + y^{2} + 6))

8 x^{3}

x y^{^{'}} + 2 y = - 2 e^{x}

x \to - 3 lim (\frac{7}{x + 3})

What is the derivative of f(t)=ln(cos(t)) ?
The derivative of f(t)=ln(cos(t)) is -tan(t)
What is the first derivative of f(t)=ln(cos(t)) ?
The first derivative of f(t)=ln(cos(t)) is -tan(t)