Question

Differentiate y w.r.t. x in the following cases:
y = sin(sinx)​

Answer 1

Step-by-step explanation:

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Answer 2

HERE IS YOUR ANSWER..

It must be mentioned w.r.t to which variable the given equation is required to be differentiated. Let me take it as w.r.t ‘x’.

Differentiating both sides w.r.t ‘x’, we get,

dy/dx=d(sin(sinx))/dx

Let us solve only the right side part of the equation which will be equal to the left part:

Let t=sinx

=> d(sin(t))/dx = (cos(t)).(dt/dx) (since differentiation of sine function gives cosine function)

Now, substituting the value of ‘t’ in the above equation, we get,

d(sin(sinx))/dx = (cos(sinx)).(d(sinx)/dx) (since differentiation of sine function gives cosine function)

=> d(sin(sinx))/dx = (cos(sinx)).(cosx)

=> dy/dx = cos(sinx) . (cosx)

Thank you…