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If y=(1)/(sqrt(a^(2)-x^(2)), find (dy)/(...

If `y=(1)/(sqrt(a^(2)-x^(2))`, find `(dy)/(dx)`.

Text Solution

Verified by Experts

Put `(a^(2) - x^(2)) = t`,so that `y = (1)/(sqrt(t)) = t^(-1//2)` and `t = (a^(2) - x^(2))`.
`:. (dy)/(dt) = - 1/2 t^(-3//2)` and `(dt)/(dx) = - 2x`.
So, `(dy)/(dx) = ((dy)/(dt) xx (dt)/(dx))`
`= (-1/2 t^(-3//2)) (-2x) = xt^(-3//2) = x(a^(2) -x^(2))^(-3//2)`.
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