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Math Help - y=f(sinx)

  1. #1
    Boo
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    y=f(sinx)

    Hello!
    Please if I have y=f(sinx)

    then
    y'(x) should be f'(sinx)cosx
    y''(x)= f''(sinx) cos x+f'(sinx)(-sinx)
    y'''(x)= f'''(x)-2f''(sinx)sinx-f'(sinx)cos x

    Is that correct?
    The problem is I shoudl get
    y'''(x)=f'''(sinx)cos^3x-3cosxsinxf''(sinx)-f'(sinx)cosx

    where did I make the mistake?
    Many thanks!!!
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  2. #2
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    Re: y=f(sinx)

    Quote Originally Posted by Boo View Post
    Hello!
    Please if I have y=f(sinx)

    then
    y'(x) should be f'(sinx)cosx
    y''(x)= f''(sinx) cos x+f'(sinx)(-sinx)
    where did I make the mistake?

    y''=f''(\sin(x))\cos^2(x)-\sin(x)f'(\cos(x))
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  3. #3
    Boo
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    Re: y=f(sinx)

    Hello, Plato!
    Thank You!
    I understand how U got f''(sin(x))cos^2(x)
    it is chain rule.

    But how did U get -sin(x)f'(cosx)?

    I tzhought it is now the product rule:
    (f'x(x)cosx)) so we should have f1'(x)f2(x)+f1(x)f2'(x)???
    Is it ok?
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    Re: y=f(sinx)

    y=f(sinx)-third-derivative.png
    Thanks from Boo
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  5. #5
    Boo
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    Re: y=f(sinx)

    Thank You, Plato and Ibdutt!
    You are life-saving!!!
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