Question

Not sure why I forgot but I can't seem to figure out how to find the derivative of this. Can anyone help?

f[x]= C/(x-1)....

I know the answer I just need the steps to refresh my memory. thanks

Answer 1

do you recall the
derivative of 1/x?

Answer 2

-1/x^(-2)

Answer 3

| Factor out constants:
= | c (d/dx(1/(x-1)))
| Use the chain rule, d/dx(1/(x-1)) = d/( du)1/u ( du)/( dx), where u = x-1 and d/( du)1/u = -1/u^2:
= | c (-(d/dx(x-1))/(x-1)^2)
| Differentiate the sum term by term:
= | -(c (d/dx(x)+d/dx(-1)))/(x-1)^2
| The derivative of -1 is zero:
= | -(c (d/dx(x)+0))/(x-1)^2
| The derivative of x is 1:
= | (c -1 × 1)/(x-1)^2

Answer 4

f[x]= C/(x-1). = c(x-1)^-1
f'(x)= -c(x-1)^-2 = -c/(x-1)^2