What is the derivative of-5ln(cos(x)) ?

The derivative of-5ln(cos(x)) is 5tan(x)

What is the first derivative of-5ln(cos(x)) ?

The first derivative of-5ln(cos(x)) is 5tan(x)

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\frac{d}{d x} (- 5 ln (cos (x)))

5 tan (x)

Solution steps

\frac{d}{d x} (- 5 ln (cos (x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 5 \frac{d}{d x} (ln (cos (x)))

Apply the chain rule:

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

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

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

= - 5 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

- 5 \cdot \frac{1}{cos ( x )} (- sin (x)) : 5 tan (x)

= 5 tan (x)

\int_{- 5}^{5} \frac{1}{v} d v

\int e^{3 x} \cdot e^{3 x} - 4 d x

t e^{- t} cos (5 t)

f (x) = sin (9 x) + cos (2 x)

\frac{d}{d x} (sec (x) - tan (x))

What is the derivative of-5ln(cos(x)) ?
The derivative of-5ln(cos(x)) is 5tan(x)
What is the first derivative of-5ln(cos(x)) ?
The first derivative of-5ln(cos(x)) is 5tan(x)