If $3 f(\cos x) + 2 f(\sin x) = 5 x$,then $f^{\prime}(\cos x) + f^{\prime}(\sin x) =$

Let $f : R \rightarrow R$ and $g : R \rightarrow R$ be two non-constant differentiable functions. If $f^{\prime}(x) = e^{(f(x)-g(x))} g^{\prime}(x)$ for all $x \in R$,and $f(1) = g(2) = 1$,then which of the following statement$(s)$ is (are) $TRUE$?

If ${x^{2/3}} + {y^{2/3}} = {a^{2/3}}$,then $\frac{dy}{dx} = $

If $y=1+xe^y$,then $\frac{dy}{dx}=$

If $a f(x)+b f\left(\frac{1}{x}\right)=x+1$, and $\frac{d}{d x}\left(x^2 f(x)\right)=2 x^2+2 x+\frac{1}{3}$, then $a-b=$

Let $f : R \to R$ be a twice differentiable function satisfying $f(0) = f(1) = 0$ and $f'(x) = f^2(x)$ for all $x \in R$. Then $\lim_{x \to 2} (f(x) + xf'(x) + x^2f''(x))$ is equal to: