How do you differentiate #g(x) = (5x^6 - 4) sin(3x)# using the product rule?
1 Answer
Mar 9, 2016
Explanation:
The Product Rule:
#frac{"d"}{"d"x}(uv) = v frac{"d"u}{"d"x} + u frac{"d"v}{"d"x}#
In this question,
#u = 5x^6-4#
#frac{"d"u}{"d"x} = 30x^5#
#v = sin(3x)#
#frac{"d"v}{"d"x} = 3cos(3x)#
So,
#f'(x) = v frac{"d"u}{"d"x} + u frac{"d"v}{"d"x}#
#= sin(3x) * (30x^5) + (5x^6-4) * (3cos(3x))#
#= 30x^5sin(3x) + 3(5x^6-4) cos(3x)#
