Question

Help with Chain Rule

Answer 1

\[y=(4x+3)^{4}(x+1)^{-3}\]

Answer 2

\[\frac{ dy }{dx }=-3(4x+3)^{4}(x+1)^{-4}+16(4x+13)^{3}(x+1)^{-3}\]

Answer 3

\[\frac{ dy }{ dx }=\frac{ (4x+3)^{3} }{ (x+1)^{4}}[-3(4x+3)+16(x+1)\]

Answer 4

how does the (x+1)^-3 factor out to leave 16(x+1) ?

Answer 5

final answer is \[\frac{ dy }{ dx }=\frac{ (4x)+3)^{3}(4x+7) }{ (x+1)^{4} }\] which I understand how to get once it gets to the form above.