How do you differentiate #y=(5+3x^-2)(4x^5+6x^3+10)# using the product rule?

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Answer 1 · 2018-06-24T17:22:27

#100x^4+126x^2+54-60x^(-3)#

We are using the product rule

#(uv)'=u'v+uv'#

with
#u=5+3x^(-2)#
we get
#u'=-6x^(-3)#

and
#v=4x^5+6x^3+10#

#v'=20x^4+18x^2#

so we get

#-6x^(-3)(4x^5+6x^3+10)+(5+3x^(-2))(4x^5+6x^3+10)#

multiplying out:

#-24x^2-36-60x^(-3)+100x^4+60x^2+90x^2+54#

combining like Terms

#100x^4+126x^2+54-60x^(-3)#