# How do you differentiate #g(x) = sin(6x)(x^2-4)# using the product rule?

##### 1 Answer

Feb 23, 2016

#### Explanation:

using the

#color(blue)" Product rule and chain rule "# If g(x) = f(x)h(x) then g'(x) = f(x)h'(x) + h(x)f'(x)

#color(red)" chain rule " : d/dx[f(g(x))] = f'(g(x)) g'(x)# hence g'(x)

#= sin6x d/dx(x^2-4) + (x^2-4) d/dx(sin6x)#

# = sin6x(2x) + (x^2-4)(cos6x) d/dx(6x)#

# = 2xsin6x + (x^2 -4)cos6x (6) #

# = 2xsin6x + 6(x^2-4)cos6x#