Understanding the Derivative of f(z)=1/(z^2+1)

[PatTheBunny]

I don't know why I'm stuck on this problem or why I keep getting it wrong. The answer in my book is -2z/(z^2+1)^2, but I ended up with -(z^2+1)(2z)/(z^2+1)^2

I don't understand where the whole z^2+1 in the numerator goes to. Isn't that how it's supposed to be chained? g(x) multiplied by g'(x)?

Here's the work:

0(z^2+1) - (1)(z^2+1)(2z)/(z^2+1)^2

-(z^2+1)(2z)/(z^2+1)^2

Could someone explain what I'm doing wrong?

 

[δοτ]

Absolutely nothing other than simplifying. Think cancel.

 

[Dick]

I don't know why I'm stuck on this problem or why I keep getting it wrong. The answer in my book is -2z/(z^2+1)^2, but I ended up with -(z^2+1)(2z)/(z^2+1)^2

I don't understand where the whole z^2+1 in the numerator goes to. Isn't that how it's supposed to be chained? g(x) multiplied by g'(x)?

Here's the work:

0(z^2+1) - (1)(z^2+1)(2z)/(z^2+1)^2

-(z^2+1)(2z)/(z^2+1)^2

Could someone explain what I'm doing wrong?

Where did the z^2+1 come from in your second term in the numerator? You just want g'(x). That doesn't need a chain rule.