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Popular >

derivative of 5cos(6ln(x))

Solution

\frac{d}{d x} (5 cos (6 ln (x)))

Solution

- \frac{30 sin ( 6 ln ( x ) )}{x}

Solution steps

\frac{d}{d x} (5 cos (6 ln (x)))

Take the constant out:

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

= 5 \frac{d}{d x} (cos (6 ln (x)))

Apply the chain rule:

- sin (6 ln (x)) \frac{d}{d x} (6 ln (x))

= - sin (6 ln (x)) \frac{d}{d x} (6 ln (x))

\frac{d}{d x} (6 ln (x)) = \frac{6}{x}

= 5 (- sin (6 ln (x)) \frac{6}{x})

Simplify

5 (- sin (6 ln (x)) \frac{6}{x}) : - \frac{30 sin ( 6 ln ( x ) )}{x}

= - \frac{30 sin ( 6 ln ( x ) )}{x}

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Frequently Asked Questions (FAQ)

What is the derivative of 5cos(6ln(x)) ?
The derivative of 5cos(6ln(x)) is -(30sin(6ln(x)))/x
What is the first derivative of 5cos(6ln(x)) ?
The first derivative of 5cos(6ln(x)) is -(30sin(6ln(x)))/x