What is the derivative of cos(ln(6x)) ?

The derivative of cos(ln(6x)) is -(sin(ln(6x)))/x

What is the first derivative of cos(ln(6x)) ?

The first derivative of cos(ln(6x)) is -(sin(ln(6x)))/x

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\frac{d}{d x} (cos (ln (6 x)))

- \frac{sin ( ln ( 6 x ) )}{x}

Solution steps

\frac{d}{d x} (cos (ln (6 x)))

Apply the chain rule:

- sin (ln (6 x)) \frac{d}{d x} (ln (6 x))

= - sin (ln (6 x)) \frac{d}{d x} (ln (6 x))

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= - sin (ln (6 x)) \frac{1}{x}

Simplify

- sin (ln (6 x)) \frac{1}{x} : - \frac{sin ( ln ( 6 x ) )}{x}

= - \frac{sin ( ln ( 6 x ) )}{x}

\int \frac{1}{( z ^{2} - 6 z + 18 ) ^{\frac{3}{2}}} d z

x \to 0 lim (- 1)

e^{x^{7}}

x^{2} y^{^{''}} + x y^{^{'}} + 4 = 0

y^{^{''}} + 7 y^{^{'}} - 3 y = 0, y (0) = - 3, y^{^{'}} (0) = 7

What is the derivative of cos(ln(6x)) ?
The derivative of cos(ln(6x)) is -(sin(ln(6x)))/x
What is the first derivative of cos(ln(6x)) ?
The first derivative of cos(ln(6x)) is -(sin(ln(6x)))/x