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Popular >

derivative of 4cos(5ln(x))

Solution

derivative of

4 cos (5 ln (x))

Solution

- \frac{20 sin ( 5 ln ( x ) )}{x}

Solution steps

\frac{d}{d x} (4 cos (5 ln (x)))

Take the constant out:

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

= 4 \frac{d}{d x} (cos (5 ln (x)))

Apply the chain rule:

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

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

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

= 4 (- sin (5 ln (x)) \frac{5}{x})

Simplify

4 (- sin (5 ln (x)) \frac{5}{x}) : - \frac{20 sin ( 5 ln ( x ) )}{x}

= - \frac{20 sin ( 5 ln ( x ) )}{x}

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Frequently Asked Questions (FAQ)

What is the derivative of 4cos(5ln(x)) ?
The derivative of 4cos(5ln(x)) is -(20sin(5ln(x)))/x
What is the first derivative of 4cos(5ln(x)) ?
The first derivative of 4cos(5ln(x)) is -(20sin(5ln(x)))/x