Here's the question you clicked on:
burhan101
Derivative of tanx²
But i dont get how its chain rule
its tanx² not (tanx)² :S
The chain rule can be applied to composites of more than two functions. consider : \[y = \tan (x ^{2})\] as: \[y = f(u) = \tan (u)\] and \[u = g(x) = x ^{2}\]
so first of all, how are your derivative skills? whats the derivative of g(x) above...?
@burhan101 ... whats the derivative of u... ? (thats the g(x) one)...
yeah, pretty much... but in this case u refers to the function g(x) which is x^2 is derivative of u = 2x... not 2u, you got the right idea tho ;)
cool, next we do the derivative of tan (u) (answwer in this case will contain a U)
so derivative of f(u) =...?
k, if u come back, its a chain rule problem, so: differentiate x^2 (2x) then differentiate tan x^2 (derivative of tan = sec^2) and multiply your results \[y' = 2x \times \sec ^{2}(x ^{2})\]