What is the derivative of cos(ln(9x)) ?

The derivative of cos(ln(9x)) is -(sin(ln(9x)))/x

What is the first derivative of cos(ln(9x)) ?

The first derivative of cos(ln(9x)) is -(sin(ln(9x)))/x

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\frac{d}{d x} (cos (ln (9 x)))

- \frac{sin ( ln ( 9 x ) )}{x}

Solution steps

\frac{d}{d x} (cos (ln (9 x)))

Apply the chain rule:

- sin (ln (9 x)) \frac{d}{d x} (ln (9 x))

= - sin (ln (9 x)) \frac{d}{d x} (ln (9 x))

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

= - sin (ln (9 x)) \frac{1}{x}

Simplify

- sin (ln (9 x)) \frac{1}{x} : - \frac{sin ( ln ( 9 x ) )}{x}

= - \frac{sin ( ln ( 9 x ) )}{x}

\frac{d}{d x} (e^{x} (13 x^{2} - 26 x + 26))

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 0

\frac{\partial}{\partial x} (y sin (\frac{x}{y}))

f (x) = \frac{x ^{2} - 6 x + 1}{x ^{2} + 4}

\int (x + 3)^{2} (2 - x)^{5} d x

What is the derivative of cos(ln(9x)) ?
The derivative of cos(ln(9x)) is -(sin(ln(9x)))/x
What is the first derivative of cos(ln(9x)) ?
The first derivative of cos(ln(9x)) is -(sin(ln(9x)))/x