How do you use the chain rule to differentiate #y=(-x^4-3)^-2#?

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Answer 1 · 2017-06-03T04:57:53

#y' = 8 x^(3) (- x^(4) - 3)^(- 3)#

We have: #y = (- x^(4) - 3)^(- 2)#

Let #u = - x^(4) - 3 Rightarrow u' = - 4 x^(3)# and #v = u^(- 2) Rightarrow v' = - 2 u^(- 3)#:

#Rightarrow y' = u' cdot v'#

#Rightarrow y' = (- 4 x^(3)) cdot (- 2 u^(- 3))#

#Rightarrow y' = 8 x^(3) u^(- 3)#

Let's replace #u# with #- x^(4) - 3#:

#Rightarrow y' = 8 x^(3) (- x^(4) - 3)^(- 3)#