Question

Differentiate y=cos^−1(cosx+sinx/√2) ​

Answer 1

Answer:

What is the derivative of y=cos−1(cosx+sinx√2) ?

Let y = Cos^-1 [(cos x+ sin x)/sq rt 2]

= cos^-1 [cos x (1/sq rt 2)+ sin x (1/ sq rt 2)]

= cos^-1 [cos x cos π/4 + sin x sin π/4]

= cos^-1 [cos (x -π/4] = x - π/4

So y = x - π/4.

Hence dy/dx = 1

Step-by-step explanation:

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Answer 2

Answer:

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