# How do you find the derivative of #f(x) = cos(pi/2)x# using the chain rule?

##### 1 Answer

For the function formulated in the question, the derivative is

However, the question might have meant this derivative instead:

#### Explanation:

If you meant the function the way that you had typed it, then

#cos(pi/2) = 0# .

Thus,

#f(x) = cos(pi/2) * x = 0 * x = 0#

You don't need the chain rule for this one since the derivative of

======================

You might have also meant

#f(x) = cos(pi/2 x) #

instead.

In this case, you can apply the chain rule as follows:

#f(x) = cos(color(blue)(u)) " where " color(blue)(u) = pi/2 x#

The derivative of

#f'(x) = [cos u]' * u'#

It holds

#[cos u]' = - sin u = - sin (pi/2 x)#

#[u]' = [pi/2 x ]' = pi/2#

Thus, your derivative is

#f'(x) = [cos u]' * u' = - pi/2 sin(pi/2 x)#