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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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