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Popular >

derivative of-3ln(cos(x/3))

Solution

\frac{d}{d x} (- 3 ln (cos (\frac{x}{3})))

Solution

tan (\frac{x}{3})

Solution steps

\frac{d}{d x} (- 3 ln (cos (\frac{x}{3})))

Take the constant out:

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

= - 3 \frac{d}{d x} (ln (cos (\frac{x}{3})))

Apply the chain rule:

\frac{1}{cos ( \frac{x}{3} )} \frac{d}{d x} (cos (\frac{x}{3}))

= \frac{1}{cos ( \frac{x}{3} )} \frac{d}{d x} (cos (\frac{x}{3}))

\frac{d}{d x} (cos (\frac{x}{3})) = - sin (\frac{x}{3}) \frac{1}{3}

= - 3 \cdot \frac{1}{cos ( \frac{x}{3} )} (- sin (\frac{x}{3}) \frac{1}{3})

Simplify

- 3 \cdot \frac{1}{cos ( \frac{x}{3} )} (- sin (\frac{x}{3}) \frac{1}{3}) : tan (\frac{x}{3})

= tan (\frac{x}{3})

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Frequently Asked Questions (FAQ)

What is the derivative of-3ln(cos(x/3)) ?
The derivative of-3ln(cos(x/3)) is tan(x/3)
What is the first derivative of-3ln(cos(x/3)) ?
The first derivative of-3ln(cos(x/3)) is tan(x/3)