How do you use the chain rule to differentiate #y=-5/(3x^2-4)^6#?

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Answer 1 · 2017-08-04T13:48:12

#dy/dx = (180x)/(3x^2-4)^5#

Name #v = x^2# and #u = (3x^2-4)# so that:

#y = -5u^(-6)#

#u = 3v-4#

Applying the chain rule:

#dy/dx = dy/(du) xx (du)/(dv) xx (dv)/dx#

#dy/dx = 30u^(-5) xx 3 xx 2x#

#dy/dx = (180x)/(3x^2-4)^5#