Suppose a differentiable function f(x) satisfies the identity f(x+y)=f(x)+f(y)+x y^2+x^2 y, for all real x and y. If lim_x → 0 (f(x))/x=1, then…

Suppose a differentiable function $\displaystyle f(x)$ satisfies the identity $\displaystyle f(x+y)=f(x)+f(y)+x y^2+x^2 y$, for all real $\displaystyle x$ and $\displaystyle y$. If $\displaystyle \lim _{x \rightarrow 0} \frac{f(x)}{x}=1$, then $\displaystyle f^{\prime}(3)$ is equal to \_\_\_\_.