Question

diffrentiate cos (x+a)
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Answer 1

Step-by-step explanation:

We have y=y=cos(x+y)cos(x+y)

Differentiating, dydx=−sin(x+y)(x+y)′dydx=−sin⁡(x+y)(x+y)′ [Chain rule]

⇒dydx=−sin(x+y)(1+dydx)⇒dydx=−sin⁡(x+y)(1+dydx)

Rewriting, dydx=−sin(x+y)−sin(x+y)⋅dydxdydx=−sin⁡(x+y)−sin⁡(x+y)⋅dydx

⇒dydx+sin(x+y)dydx=−sin(x+y)⇒dydx+sin⁡(x+y)dydx=−sin⁡(x+y)

Taking dydxdydx common,

dydx(1+sin(x+y))=−sin(x+y)dydx(1+sin⁡(x+y))=−sin⁡(x+y)

Bringing (1+sin(x+y))(1+sin⁡(x+y)) to other side,