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anonymous

  • 5 years ago

find the derivative of sin^4 (x)

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  1. anonymous
    • 5 years ago
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    would it be cos^4x?

  2. anonymous
    • 5 years ago
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    i no that the derivative of sin is cos, but the power of 4 confuses me

  3. anonymous
    • 5 years ago
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    you can split it up sin^2x * sin^2x than do power reducing

  4. anonymous
    • 5 years ago
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    \[\frac{d}{dx}\sin^2 x=4 \sin ^3 x .\cos x\]

  5. anonymous
    • 5 years ago
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    sin^4 x sorry

  6. anonymous
    • 5 years ago
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    Have you learned about the chain rule yet?

  7. anonymous
    • 5 years ago
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    Rewrite it as (cosx)^4

  8. anonymous
    • 5 years ago
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    ya i learned the chain rule

  9. anonymous
    • 5 years ago
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    Oops (sinx)^4

  10. anonymous
    • 5 years ago
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    Just like newone wrote and chain rule it.

  11. anonymous
    • 5 years ago
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    so it would be 4sinx^3 * cos?

  12. anonymous
    • 5 years ago
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    yes

  13. anonymous
    • 5 years ago
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    ok so what happens here is this. you have to use chain rule. soo.... sin^4(x) --> 4sin^3(x)cos(x)

  14. anonymous
    • 5 years ago
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    you can even check it out in wolframalpha

  15. anonymous
    • 5 years ago
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    so how do i no when to use the chainrule?

  16. myininaya
    • 5 years ago
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    when you have a function inside a function

  17. anonymous
    • 5 years ago
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    so for this question sin is the inside function and 4 is the outside?

  18. myininaya
    • 5 years ago
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    so we have f(g(x))=(sinx)^4 where f(x)=x^4 and g(x)=sinx

  19. anonymous
    • 5 years ago
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    ooooo i c!!

  20. myininaya
    • 5 years ago
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    the chain rule is this f'(g(x))*g'(x)

  21. anonymous
    • 5 years ago
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    ok. think about it like this. when you find derivative of x^2 its 2x. we stop right here becuase we note that x is not in any function. say if we have cos(2x) then we have to use chain rule. becuase x is inside another function. so derivative of cos(2x) = -sin(2x) = so we derivce the function first. and then we note that we have to further derive x. so we derivce 2x = 2. so we get the final answer cos(2x) = -2sin(2x) chain rule states:

  22. anonymous
    • 5 years ago
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    thank u guys!

  23. anonymous
    • 5 years ago
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    Let \[u = (sin\ x) \rightarrow (sin\ x)^4 = u^4\ and\ du/dx = cos\ x\] Following the chain rule we have \[d/dx(u^4) = d/du(u^4) * du/dx= 4u^3 * (\cos\ x) = 4(\sin\ x)^3(\cos\ x)\]

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