How do you differentiate #g(y) =(x^2 + 6) (4x^6 + 5)# using the product rule?

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Answer 1 · 2017-01-24T19:33:06

#dy/dx=2x(15x^6+72x^4+5)#

Product rule:

#f'(uv)=uv'+vu'#

#g(y)=(x^2+6)(4x^6+5)#

#g'(y)=2x(4x^6+5)+24x^5(x^2+6)#

#=8x^7+10x+24x^7+144x^5#

#=30x^7+144x^5+10x#

#=2x(15x^6+72x^4+5)#