What is the derivative of (cos(x)^{pi/5}) ?

The derivative of (cos(x)^{pi/5}) is -(pisin(x)cos^{(pi-5)/5}(x))/(5)

What is the first derivative of (cos(x)^{pi/5}) ?

The first derivative of (cos(x)^{pi/5}) is -(pisin(x)cos^{(pi-5)/5}(x))/(5)

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\frac{d}{d x} ((cos (x))^{\frac{π}{5}})

- \frac{π sin ( x ) cos ^{\frac{π - 5}{5}} ( x )}{5}

Solution steps

\frac{d}{d x} ((cos (x))^{\frac{π}{5}})

Apply the chain rule:

\frac{π ( cos ( x ) ) ^{\frac{π - 5}{5}}}{5} \frac{d}{d x} (cos (x))

= \frac{π ( cos ( x ) ) ^{\frac{π - 5}{5}}}{5} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= \frac{π ( cos ( x ) ) ^{\frac{π - 5}{5}}}{5} (- sin (x))

Simplify

\frac{π cos ^{\frac{π - 5}{5}} ( x )}{5} (- sin (x)) : - \frac{π sin ( x ) cos ^{\frac{π - 5}{5}} ( x )}{5}

= - \frac{π sin ( x ) cos ^{\frac{π - 5}{5}} ( x )}{5}

\int_{- 2}^{3} \frac{45}{x ^{4}} d x

\frac{d y}{d x} = \frac{x + y}{x + y + 2}

\int \frac{x + 5}{x ^{2} ( x - 2 )} d x

x \to 0 lim (ln (1))

e^{- 4 x} (cos (3 x))

What is the derivative of (cos(x)^{pi/5}) ?
The derivative of (cos(x)^{pi/5}) is -(pisin(x)cos^{(pi-5)/5}(x))/(5)
What is the first derivative of (cos(x)^{pi/5}) ?
The first derivative of (cos(x)^{pi/5}) is -(pisin(x)cos^{(pi-5)/5}(x))/(5)