Function second derivative evaluation (Jee Mains)

Continuity and Differentiability

Medium

Function second derivative evaluation

Let f : R → R be a twice differentiable function such that (sinx cosy)(f(2x+2y) – f(2x – 2y)) = (cosx siny)(f(2x+2y) + f(2x – 2y)), for all x, y ∈ R.
If $f\prime \left( 0 \right) = \frac{1}{2},$ then the value of 24 $f\prime \prime \left( {\frac{{5\pi }}{3}} \right)$ is :

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