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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= - sin (ln (3 x)) \frac{1}{x}

Simplify

- sin (ln (3 x)) \frac{1}{x} : - \frac{sin ( ln ( 3 x ) )}{x}

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

\int x - x d x

2 - x^{2}, - x

x \to - 1 lim (4 x^{2})

\frac{\partial}{\partial x} (4 x^{2} e^{a y} + 3 e^{b x})

\int \frac{tan ^{3} ( x )}{cos ^{3} ( x )} d x

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