What is the derivative of cos(ln(x^2)) ?

The derivative of cos(ln(x^2)) is -(2sin(2ln(x)))/x

What is the first derivative of cos(ln(x^2)) ?

The first derivative of cos(ln(x^2)) is -(2sin(2ln(x)))/x

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\frac{d}{d x} (cos (ln (x^{2})))

- \frac{2 sin ( 2 ln ( x ) )}{x}

Solution steps

\frac{d}{d x} (cos (ln (x^{2})))

Apply the chain rule:

- sin (ln (x^{2})) \frac{d}{d x} (ln (x^{2}))

= - sin (ln (x^{2})) \frac{d}{d x} (ln (x^{2}))

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

= - sin (ln (x^{2})) \frac{2}{x}

Simplify

- sin (ln (x^{2})) \frac{2}{x} : - \frac{2 sin ( 2 ln ( x ) )}{x}

= - \frac{2 sin ( 2 ln ( x ) )}{x}

2 cos (3 x)

y^{^{'}} + \frac{2 x}{1 + x ^{2}} y = \frac{e ^{- x}}{1 + x ^{2}}

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

x \to \infty lim (x^{- 1})

x^{\frac{4}{5}}

What is the derivative of cos(ln(x^2)) ?
The derivative of cos(ln(x^2)) is -(2sin(2ln(x)))/x
What is the first derivative of cos(ln(x^2)) ?
The first derivative of cos(ln(x^2)) is -(2sin(2ln(x)))/x