If y = sin-1 x + cos-1 x, find \(\cfrac{dy}{d\mathrm x}\).

1.	If y = sin-1 x + cos-1 x, find \(\cfrac{dy}{d\mathrm x}\).
Answer» We know that sin^-1x+ cos^-1x = \(\cfrac{\pi}2\) So, here y = sin^–1 x + cos^–1 x = \(\cfrac{\pi}2\) which is a constant. Also, sin^-1 x and cos^-1 x exist only when -1 ≤ x ≤ 1 So, \(\cfrac{dy}{d\mathrm x}\) = 0 when x ∈ [-1, 1] and does not exist for all other values of x.

Answer»

We know that sin^-1x+ cos^-1x = \(\cfrac{\pi}2\)

So, here y = sin^–1 x + cos^–1 x

= \(\cfrac{\pi}2\) which is a constant.

Also, sin^-1 x and cos^-1 x exist only when -1 ≤ x ≤ 1

So, \(\cfrac{dy}{d\mathrm x}\) = 0 when x ∈ [-1, 1] and does not exist for all other values of x.

Discussion

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