What is the derivative of 5cos(4ln(x)) ?

The derivative of 5cos(4ln(x)) is -(20sin(4ln(x)))/x

What is the first derivative of 5cos(4ln(x)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

- sin (4 ln (x)) \frac{d}{d x} (4 ln (x))

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

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

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

Simplify

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

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

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