Find the derivative of y with respect to a of y=tan−1(a+1) .

Answer 1

To find the derivative of y with respect to a, we can use the chain rule.

Let u = a + 1.

Then, y = tan^(-1)(u).

To find dy/da, we need to find dy/du and du/da.

dy/du = 1/(1 + u^2) * du/da

du/da = 1.

Substituting these values into the chain rule formula:

dy/da = dy/du * du/da
= (1/(1 + u^2)) * 1
= 1/(1 + (a + 1)^2)

Therefore, the derivative of y with respect to a is 1/(1 + (a + 1)^2).