Question

dy
If y = x sin x^2 , then the value of
dx/dy
is​

Answer 1

Here you need to apply product rule and chain rule.

y = f(x) = x sin (x^2)

f' = u'v + uv' (by product rule)

here, u = x and v = sin (x^2)

so, u' = 1 and v' = cos (x^2) * 2x

therefore, f' = 1 * sin(x^2) + x * cos (x^2) * 2x

                    = sin (x^2) + 2x^2 cos (x^2)