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Math Help - inversetrig.2

  1. #1
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    inversetrig.2

    differentiate f(x) =tan-1(sinx) and f(x) =cos-1(1-x^s)/(1+x^2), stating domain.

    thankyou for any help given =)
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  2. #2
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    Quote Originally Posted by iiharthero View Post
    differentiate f(x) =tan-1(sinx) and f(x) =cos-1(1-x^s)/(1+x^2), stating domain.

    thankyou for any help given =)
    Using the chain rule and the rule for the derivative of inverse functions:

    \frac{d}{dx}\arctan (\sin x)=\frac{\cos x}{1+\sin^2x}\,,\,\,\forall\,x\in \mathbb{R}

    \frac{d}{dx}\arccos \left(\frac{1-x^2}{1+x^2}\right)=-\frac{-4x}{(1+x^2)^2}\frac{1}{\sqrt{1-\frac{(1-x^2)^2}{(1+x^2)^2}}}=\frac{4}{1+x^2}\frac{1}{\sqrt  {4x^2}}=\frac{2x}{(1+x^2)|x|} \,,\,\,\forall\,x\in \mathbb{R}
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