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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

- sin (3 ln (x)) \frac{d}{d x} (3 ln (x))

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

\frac{d}{d x} (3 ln (x)) = \frac{3}{x}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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6 x^{2} sin (x) tan (x)

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