How do you differentiate #f(x)=sin(e^(3x)) # using the chain rule?

1 Answer
Mar 16, 2016

Answer:

# 3e^(3x)cos(e^(3x)) #

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)) #