How do you differentiate #f(x)=sec(8x ) # using the chain rule?

Question

How do you differentiate #f(x)=sec(8x  )  # using the chain rule?

Cameron Alexander · Accepted Answer

Please see the explanation section, below.

We know that #d/dx(secx) = secx tanx# Applying the chain rule, we have #d/dx(secu) = secutanu (du)/dx# So, in this question, since #u=8x#, we get #f'(x) = sec(8x)tan(8x) d/dx(8x)# # = 8sec(8x)tan(8x)#

Charles Anctil · Answer

undefined To differentiate f(x) = sec(8x) using the chain rule, follow these steps:

1. Identify the outer function and the inner function. In this case, the outer function is sec(x) and the inner function is 8x.
2. Apply the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.
3. The derivative of sec(x) is sec(x)tan(x).
4. The derivative of the inner function 8x is 8.
5. Multiply the derivative of the outer function by the derivative of the inner function to obtain the derivative of the composite function.
6. Therefore, the derivative of f(x) = sec(8x) is f'(x) = sec(8x)tan(8x) * 8.