What is the derivative of 3cos(5ln(x)) ?

The derivative of 3cos(5ln(x)) is -(15sin(5ln(x)))/x

What is the first derivative of 3cos(5ln(x)) ?

The first derivative of 3cos(5ln(x)) is -(15sin(5ln(x)))/x

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derivative of

3 cos (5 ln (x))

- \frac{15 sin ( 5 ln ( x ) )}{x}

Solution steps

\frac{d}{d x} (3 cos (5 ln (x)))

Take the constant out:

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

= 3 \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}

= 3 (- sin (5 ln (x)) \frac{5}{x})

Simplify

3 (- sin (5 ln (x)) \frac{5}{x}) : - \frac{15 sin ( 5 ln ( x ) )}{x}

= - \frac{15 sin ( 5 ln ( x ) )}{x}

What is the derivative of 3cos(5ln(x)) ?
The derivative of 3cos(5ln(x)) is -(15sin(5ln(x)))/x
What is the first derivative of 3cos(5ln(x)) ?
The first derivative of 3cos(5ln(x)) is -(15sin(5ln(x)))/x