Differentiation question bank (Maths)

Let $f\left(x\right)$ is a differentiable function on $x\in R$, such that $f\left(x+y\right)=f\left(x\right)f\left(y\right)$ for all $x,y\in R$ where $f\left(0\right)\ne 0.$ If $f\left(5\right)=10, f^{\text{'}}\left(0\right)=6$, then the value of $f^{\prime }\left(5\right)$ is equal to

If $f:R\to R$ is a function defined as $f\left(x^3\right)=x^5, \forall x\in R-\left\{0\right\}$ and $f\left(x\right)$ is differentiable $\forall x\in R$, then the value of $\frac{1}{4}{f}^{\text{'}}\left(27\right)$ is equal to (here $f^{\text{'}}$ represents the derivative of $f$)