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burhan101

  • 2 years ago

Derivative of tanx²

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  1. burhan101
    • 2 years ago
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    But i dont get how its chain rule

  2. burhan101
    • 2 years ago
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    its tanx² not (tanx)² :S

  3. Jack1
    • 2 years ago
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    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
    • 2 years ago
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    ooo shiny, cheers

  5. Jack1
    • 2 years ago
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    so first of all, how are your derivative skills? whats the derivative of g(x) above...?

  6. Jack1
    • 2 years ago
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    @burhan101 ... whats the derivative of u... ? (thats the g(x) one)...

  7. burhan101
    • 2 years ago
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    2u

  8. Jack1
    • 2 years ago
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    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
    • 2 years ago
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    cool, next we do the derivative of tan (u) (answwer in this case will contain a U)

  10. Jack1
    • 2 years ago
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    so derivative of f(u) =...?

  11. Jack1
    • 2 years ago
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    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 \[y' = 2x \times \sec ^{2}(x ^{2})\]

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