Differentaition problem

Question

How to differentiate $$f(x)= x+ (4/x-1)$$,$$ f’(x) = 1.(x-1)^{-1}.(-1)(1).1 $$

Is that right or there’s a better solution if right?

Any help will be appreciated.

Answer 1

write it in the form $$f(x)=x+4(x-1)^{-1}$$ and use the sum and the power rule so $$f'(x)=1-4(-1)(x-1)^{-2}$$

Answer 2

What you wrote was $x+ \frac{4}{x}- 1$. Its derivative would be $1-\frac{4}{x^2}$.

If you meant $x+ \frac{4}{x- 1}$ then the derivative is $1-\frac{4}{(x- 1)^2}$. Neither is what you wrote,