How do you differentiate #f(x)=sec(4x^5)#?
1 Answer
Aug 13, 2017
Explanation:
We're asked to find the derivative
#d/(dx) [sec(4x^5)]#
We can first use the chain rule:
#d/(dx) [sec(4x^5)] = d/(du) [secu] (du)/(dx)#
where
-
#u = 4x^5# -
#d/(du) [secu] = tanusecu# :
#= tan(4x^5)sec(4x^5)d/(dx) [4x^5]#
We now use the power rule:
#d/(dx)[x^n] = nx^(n-1)#
where
#= tan(4x^5)sec(4x^5)5(4x^4)#
#color(blue)(ulbar(|stackrel(" ")(" "20x^4tan(4x^5)sec(4x^5)" ")|)#
