The derivative of t a n - 1 s i n x - c o s x s i n x + c o s x with respect to x 2 , where x ∈ 0 ,…

The derivative of tan-1sinx-cosxsinx+cosx with respect to x2, where x∈0,π2, is
  1. 2
  2. 12
  3. 23
  4. 1

Solution

Given function can be written as

y=tan-1sinx-cosxsinx+cosx

⇒ y=tan-1tanx-1tanx+1

⇒ y=tan-1tanx-π4 given x∈0,π2
⇒ y=x-π4
Now dydx2=2dydx=2

Asked in: MHT CET Full Test 7

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