How do you use the chain rule to differentiate #(-9x^2+3x+5)^100#?

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Answer 1 · 2016-11-24T14:47:47

Let #y = u^100# and #u = -9x^2 +3x + 5#.

By the chain rule, #dy/dx= dy/(du) xx (du)/dx#.

By the power rule, #dy/(du) = 100u^99# and #(du)/dx= -18x + 3#

By the chain rule, #dy/dx= dy/(du) xx (du)/dx#:

#dy/dx = 100u^99 xx (-18x + 3)#

#dy/dx = 300(-9x^2 + 3x + 5)^99- 1800x(-9x^2 + 3x + 5)^99#

Hopefully this helps!