What is the derivative of 7ln(cos(x)) ?

The derivative of 7ln(cos(x)) is -7tan(x)

What is the first derivative of 7ln(cos(x)) ?

The first derivative of 7ln(cos(x)) is -7tan(x)

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\frac{d}{d x} (7 ln (cos (x)))

- 7 tan (x)

Solution steps

\frac{d}{d x} (7 ln (cos (x)))

Take the constant out:

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

= 7 \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)

= 7 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

7 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 7 tan (x)

= - 7 tan (x)

What is the derivative of 7ln(cos(x)) ?
The derivative of 7ln(cos(x)) is -7tan(x)
What is the first derivative of 7ln(cos(x)) ?
The first derivative of 7ln(cos(x)) is -7tan(x)