Question

Which is an expression for the derivative P(x)=1+f(x)/f(x) , where f(x) is a differentiable function?

Answer 1

\[P(x)=\frac{f(x)+1}{f(x)}\]
?

Answer 2

yes. :)

Answer 3

\[P(x)=1+\frac{1}{f(x)}\]
\[P'(x)=\frac{-f'(x)}{f^2(x)}\]

Answer 4

Re-write it as,\[P(x)=1+\frac{1}{f(x)}\]We need to use the chain rule here:\[dP/dx=\frac{dP}{df(x)}\frac{df(x)}{dx}\]This gives:\[dP/dx=\frac{-1}{f(x)^2}f \prime(x)\]

Answer 5

bravo

Answer 6

I wrote the solution a bit confusing, I mean it as:\[dP/dx=\frac{-1}{[f(x)]^2}f \prime(x)\]

Answer 7

you're the best!