Question

Find the derivatives of the following functions using the chain rule.

Answer 1

To find:

The derivative of a function:

`f(x)=(x^4+1)^(-2)`

Solution:

It is known that the chain rule of differentiation is as follows:

`(dy)/(dx)=(dy)/(du)*(du)/(dx)`

So, the differentiation of the given function is as follows:

`\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}`

Thus, the answer is:

`f^(\prime)(x)=-8x^3(x^4+1)^(-3)`