If $x^2+y^2=4$,then $y \frac{dy}{dx}+x=$

If $(x - y)e^{x/(x - y)} = k$,then:

For $x \in R$,$f(x) = |\log 2 - \sin x|$ and $g(x) = f(f(x))$,then

If $y^{\cos x}=x^{\sin y}$,then $\frac{d y}{d x}=$

Let $f: R \rightarrow R$ be a differentiable function with $f(0)=1$ and satisfying the equation $f(x+y)=f(x) \cdot f^{\prime}(y)+f^{\prime}(x) \cdot f(y)$ for all $x, y \in R$. Then the value of $\log (f(4))$ is

If $f(x) = \frac{1}{x^2} \int_3^x (2t - 3f'(t)) dt$,then $f'(3)$ is equal to