Mathematical Muscle-building:
Inverse Trigonometric Functions
Do not look in your textbooks. You may use that
d/dx (sin-1u) = (1-u2)-1/2 (du/dx)
and
d/dx (tan-1u) = (1+u2)-1 (du/dx)
(1) Find y' when
(a) y = sin-1(x2)
(b) y = sin-1(ex)
(c) y = sin-1[ e
sin-1x]
(d) [tan-1(x)](1+x2)
(2) Find y' by implicit differentiation from
(tan-1y)(x2+1) = 10.
(3) Without trying to solve for y', implicitly differentiate
sin-1(exy) = 5
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