Find `(dy)/(dx)`for `y=sin(x^2+1)dot`

1.	Find `(dy)/(dx)`for `y=sin(x^2+1)dot`
Answer» `"Let "y= sin(x^(2)+1).` Putting `u=x^(2)+1," we get y sin u"` `therefore" "(dy)/(dx)=cos u and (du)/(dx) = 2x` `"Now, "(du)/(dx)=(dy)/(du).(du)/(dx)` `= (cos u) (2x)=2x cos(x^(2)+1)`

Discussion

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If `f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta)))`, where `-pi/4 lt theta lt pi/4,` then the value of `d/(d(tantheta)) f(theta)` is