Differentiate with respect to if –1 < x < 1.
Let and
We need to differentiate u with respect to v that is find.
We have
By substituting x = tan θ, we have
Given, –1 < x < 1 ⇒ x ϵ (–1, 1)
However, x = tan θ
⇒ tan θ ϵ (–1, 1)
Hence,
On differentiating u with respect to x, we get
We know and derivative of a constant is 0.
Now, we have
On differentiating v with respect to x, we get
We know
We know and derivative of a constant is 0.
We have
Thus,