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Tricky trig derrivation

  1. Oct 22, 2007 #1
    1. The problem statement, all variables and given/known data
    Calculate the derivative of tan[tex]^{2}[/tex](sin(2x+1)[tex]^{6}[/tex])

    2. Relevant equations

    3. The attempt at a solution
    I assume this uses chain rule, by do not see how tan[tex]^{2}[/tex] can be derrived.
  2. jcsd
  3. Oct 22, 2007 #2
    Can you differentiate (tan(something))2?
  4. Oct 22, 2007 #3
    I'm not actually sure i can, this is the first time i'v come accross this kind of differentiation question i'm afraid
  5. Oct 22, 2007 #4
    If you want to do it in steps, try substituting u = tan(sin(2x + 1)6)

    The derivative of u2 where u is a function of something, say x, is


    Now you have an easier derivative (du/dx). Do this for each part of the chain.
  6. Oct 22, 2007 #5
    Use the chain rule. For example, consider the function f, which is a function of x, and which in turn is a function of t. If you want to differentiate, say [f(x(t))], use the chain rule...

    [tex]\frac{df}{dt} = \frac{df}{dx}\frac{dx}{dt}.[/tex]

    Your problem is more like f(y(x(t))), but the principle remains the same.
  7. Oct 22, 2007 #6
    tan^2(sin(2x+1)^6)//let u=2x+1
    tan^2(sin(u)^6)//use chain rule
    Last edited: Oct 22, 2007
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