Derivative of tanx²

Question

Derivative of tanx²

anonymous · Answer

But i dont get how its chain rule

anonymous · Answer

its tanx² not (tanx)² :S

jack1 · Answer

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 

$$u = g(x) = x ^{2}$$

jack1 · Answer

ooo shiny, cheers

jack1 · Answer

so first of all, how are your derivative skills?
whats the derivative of g(x) above...?

jack1 · Answer

@burhan101 ... whats the derivative of u... ?

(thats the g(x) one)...

anonymous · Answer

2u

jack1 · Answer

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 ;)

jack1 · Answer

cool, next we do the derivative of tan (u)   (answwer in this case will contain a U)

jack1 · Answer

so derivative of f(u) =...?

jack1 · Answer

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     

$$y' = 2x \times \sec ^{2}(x ^{2})$$