Let $f\left(x\right)=x^5+2x^3+3x+4$ then the value of $28\frac{d}{dx}\left(f^{-1}\left(x\right)\right)\text{ at }x=-2$ is 

$f\left(x\right)=x^5+2x^3+3x+4$

$f\text{'}\left(x\right)=5x^4+6x^2+3$

$f\left(x\right)=-2\Rightarrow x=-1$

$f\text{'}\left(-1\right)=5+6+3=14$

$\text{let }g\left(x\right)\text{ is the inverse of function }f\left(x\right)\text{, }$

$g\circ f\left(x\right)=x\Rightarrow g^1\left(f\right(x\left)\right)f^1\left(x\right)=1$$\Rightarrow g^1\left(f\right(x\left)\right)=\frac{1}{f^1\left(x\right)}$

$\Rightarrow g^1(-2)=\frac{1}{f^1(-1)}=\frac{1}{14}$

$28\frac{d}{dx}\left(f^{-1}\left(x\right)\right)\text{ at }x=-2 is 28\times \frac{1}{14}=2$