Question

What is the derivative of `1/(1 + x^4)^(1/2)`?

Answer 1

`(-2x^3)/(1+x^4)^(3/2)`

Solution:

rewrite: `1/(1 + x^4)^(1/2) = (1+x^4)^(-1/2)`

Now use the power rule and the chain rule (a combination sometimes called the generalized power rule)

The derivative is:

`-1/2 (1+x^4)^(-3/2) (4x^3) = (-2x^3)/(1+x^4)^(3/2)`

Answer 2

The answer is:

This function can be written in this way:

`y=(1+x^4)^(-1/2)rArr`

`y'=-1/2(1+x^4)^(-1/2-1)*4x^3=-(2x^3)/sqrt((1+x^4)^3)`.