Derivative of inverse trigonometric functions

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  1. Review: what are "inverse trigonometric functions" ?

    Find the measure of angle θ\theta to the nearest degree:
    Derivative of inverse trigonometric functions
    1. Use implicit differentiation to prove the formula:
      ddx(sin1x)=11x2\frac{{d}}{{{d}x}}\left( {{{\sin }^{ - 1}}x} \right) = \frac{1}{{\sqrt {1 - {x^2}} }}
      1. Calculate the derivative of y=y= arccos (x2)(x^2)
        1. Calculate the derivative of y=4y=4 arccot (3x+1)(3x+1)
          1. Calculate the derivative of y=4arctan(ex)x2y= \frac{4 \arctan (e^x)}{x^2}
            1. Calculate the derivative of y=y= arcsec  x  \; x \; arccsc  x\; x
              1. Prove that ddx[tan1(4x2)+cot1(4x2)]=0\frac{d}{dx} [\tan^{-1}(4x^2)+ \cot^{-1}(4x^2)]=0