What is the derivative of ln(cos(1/x)) ?

The derivative of ln(cos(1/x)) is (tan(1/x))/(x^2)

What is the first derivative of ln(cos(1/x)) ?

The first derivative of ln(cos(1/x)) is (tan(1/x))/(x^2)

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\frac{d}{d x} (ln (cos (\frac{1}{x})))

\frac{tan ( \frac{1}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (ln (cos (\frac{1}{x})))

Apply the chain rule:

\frac{1}{cos ( \frac{1}{x} )} \frac{d}{d x} (cos (\frac{1}{x}))

= \frac{1}{cos ( \frac{1}{x} )} \frac{d}{d x} (cos (\frac{1}{x}))

\frac{d}{d x} (cos (\frac{1}{x})) = \frac{sin ( \frac{1}{x} )}{x ^{2}}

= \frac{1}{cos ( \frac{1}{x} )} \cdot \frac{sin ( \frac{1}{x} )}{x ^{2}}

Simplify

\frac{1}{cos ( \frac{1}{x} )} \cdot \frac{sin ( \frac{1}{x} )}{x ^{2}} : \frac{tan ( \frac{1}{x} )}{x ^{2}}

= \frac{tan ( \frac{1}{x} )}{x ^{2}}

\frac{d y}{d x} = e^{5 x} + 8 y

y^{3} - (2 x + 4) + 3 x y^{2} y^{^{'}} = 0

7 cos (2 x), 7 sin (4 x), x = 0, x = \frac{π}{4}

2 x^{3} + 3 x^{2} - 12 x + 2

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

What is the derivative of ln(cos(1/x)) ?
The derivative of ln(cos(1/x)) is (tan(1/x))/(x^2)
What is the first derivative of ln(cos(1/x)) ?
The first derivative of ln(cos(1/x)) is (tan(1/x))/(x^2)