How do you differentiate #f(x)=sin(e^(3x)) # using the chain rule?
1 Answer
Mar 16, 2016
Explanation:
Using the
#color(blue)" chain rule " #
# d/dx [ f(g(x)) ] = f'(g(x)) . g'(x) # and the standard derivatives:
#d/dx(e^x) = e^x , d/dx(sinx) = cosx# hence f'(x)
#=cos(e^(3x)) . d/dx(e^(3x))#
# = cos(e^(3x)). e^(3x). d/dx(3x) = 3e^(3x)cos(e^(3x)) #
