How do you differentiate #g(x) = (5x^6 - 4) sin(3x)# using the product rule?

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Answer 1 · 2016-03-09T03:46:41

#f'(x) = 30x^5sin(3x) + 3(5x^6-4) cos(3x)#

#frac{"d"}{"d"x}(uv) = v frac{"d"u}{"d"x} + u frac{"d"v}{"d"x}#

In this question,

#frac{"d"u}{"d"x} = 30x^5#

#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)#