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Popular >

derivative of f(x)=-5ln(sin(x))

Solution

derivative of

f (x) = - 5 ln (sin (x))

Solution

- 5 cot (x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - 5 cot (x)

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=-5ln(sin(x)) ?
The derivative of f(x)=-5ln(sin(x)) is -5cot(x)
What is the first derivative of f(x)=-5ln(sin(x)) ?
The first derivative of f(x)=-5ln(sin(x)) is -5cot(x)