SOLUTION: Find the derivative of the function, Solution or Explanation y = (tan^−1(4x))^2

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Question 1156570: Find the derivative of the function, Solution or Explanation
y = (tan^−1(4x))^2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+%28tan%5E-1%284x%29%29%5E2
apply the chain rule : df%28u%29%2Fdx=%28df%2Fdu%29%2A+%28du%2Fdx%29
where f=u%5E2 and u=tan%5E-1%284x%29

df%28u%29%2Fdx=%28d%2Fdu%29%28u%5E2%29%2A+%28du%2Fdx%29%28tan%5E-1%284x%29%29
%28d%2Fdu%29%28u%5E2%29=2u
%28du%2Fdx%29%28tan%5E-1%284x%29%29=4%2F%2816x%5E2%2B1%29

df%28u%29%2Fdx=y'

y'=2u%2A+%284%2F%2816x%5E2%2B1%29%29

substitute back u=tan%5E-1%284x%29

y'=2tan%5E-1%284x%29%2A+%284%2F%2816x%5E2%2B1%29%29

y'=%288tan%5E-1%284x%29%29%2F%2816x%5E2%2B1%29%29