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

The derivative of ln|cos(pi/x |) is (pitan(pi/x))/(x^2)

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

The first derivative of ln|cos(pi/x |) is (pitan(pi/x))/(x^2)

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\frac{d}{d x} (ln cos (\frac{π}{x}))

\frac{π tan ( \frac{π}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (ln cos (\frac{π}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{4} 5 d x

\int \frac{x ^{3}}{x ^{2} - 1} d x

25 - x^{2} d x

\frac{\partial}{\partial y} (x e^{2 yz})

\frac{\partial}{\partial s} (\frac{s}{s ^{2} + t ^{2}})

What is the derivative of ln|cos(pi/x |) ?
The derivative of ln|cos(pi/x |) is (pitan(pi/x))/(x^2)
What is the first derivative of ln|cos(pi/x |) ?
The first derivative of ln|cos(pi/x |) is (pitan(pi/x))/(x^2)