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B What's the derivative of sin^3(x+1) ^2?

  1. Dec 31, 2017 #1
    • Member warned that HW posts must include some effort
    Can someone explain it to me step by step?
     
  2. jcsd
  3. Dec 31, 2017 #2

    FactChecker

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    Add parenthesis to show clearly what the equation is and what the exponents are applied to.
     
  4. Dec 31, 2017 #3
     

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  5. Dec 31, 2017 #4

    FactChecker

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    You can apply the chain rule repeatedly to (sin((x+1)2))3 = f(g(h(x))), where f(g) = g3, g(h)=sin(h), and h(x)=(x+1)2.

    The overall equation is
    df/dx = df/dg|g ⋅ dg/dh|h ⋅ dh/dx

    df/dg = 3g2; dg/dh = cos(h); dh/dx = 2(x+1).

    Substituting in gives df/dx = 3(sin((x+1)2))2 ⋅ cos((x+1)2) ⋅ 2(x+1)
     
  6. Dec 31, 2017 #5
    Thank you!
     
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