To find:
The derivative of a function:
[tex]f(x)=(x^4+1)^{-2}[/tex]
Solution:
It is known that the chain rule of differentiation is as follows:
[tex]\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}[/tex]
So, the differentiation of the given function is as follows:
[tex]\begin{gathered} f^{\prime}(x)=((x^4+1)^{-2})^{\prime} \\ =-2(x^4+1)^{-3}(x^4+1)^{\prime} \\ =-2(x^4+1)^{-3}(4x^3) \\ =-8x^3(x^4+1)^{-3} \end{gathered}[/tex]
Thus, the answer is:
[tex]f^{\prime}(x)=-8x^3(x^4+1)^{-3}[/tex]
