How do you find the derivative of #tan^4 (x)#?
1 Answer
May 19, 2017
By using the power rule
#d/(dx)[(u(x))^n] = n [u(x)]^(n-1)# , where#u(x)# is a function of#x# ,
and the chain rule
#d/(dx)[f(u)] = (df)/(du)(du)/(dx)# , where#f = f(u(x))# .
If we rewrite
#f(u) = u^4# #u(x) = tanx#
As a result:
#color(blue)(d/(dx)[f(u)]) = (df)/(du)(du)/(dx)#
#d/(du)[u^4]cdot d/(dx)[tanx]#
#= 4u^3 cdot sec^2x#
#= color(blue)(4tan^3xsec^2x)#
