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March 27, 2017

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How do you do the derivative of an inverse trig function?

arcsin (sqrt2/2)??

  • Calc - ,

    arcsin(sqrt2/2 ) is a constant. The derivative of a constant is zero.

  • Calc - ,

    oops mixed up 2 questionss haha

  • Calc - ,

    to find an arcsin you would just have to memorize the unit circle right? so arccos of -sqrt3/2 is 5pi/6?

  • Calc - ,

    yes, that is the easy way.

  • Calc - ,

    However, to find the derivative of an inverse trig function, go through the back door, as it were

    y = arcsin(x)
    sin y = x
    cos y y' = 1
    y' = 1/cos x = 1/√(1-sin2x) = 1/√(1-x2)

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