burhan101 2 years ago Derivative of tanx²

1. burhan101

But i dont get how its chain rule

2. burhan101

its tanx² not (tanx)² :S

3. Jack1

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

4. Jack1

ooo shiny, cheers

5. Jack1

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

6. Jack1

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

7. burhan101

2u

8. Jack1

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 ;)

9. Jack1

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

10. Jack1

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

11. Jack1

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