Question

Differentiate the function f(z)=(1-1/z)^5

Answer 1

first rewrite the expression
f(z) = ( 1 - z^-1 ) ^5

f ' (z) = 5 ( 1 - z^ -1 ) ^ 4 * ( -(-1)*z^-2))

Answer 2

Simplify and apply quotient rule

Answer 3

you can use chain rule

Answer 4

\[\frac{ d }{ dx } u^n = n u ^{n-1}u'\]

Answer 5

Where in your case u = the function inside ( ) and u' is the derivative of that function

Answer 6

f ' (z) = 5 ( 1 - z^ -1 ) ^ 4 * ( -(-1)*z^-2))

f ' (z) = 5 ( 1 - z^ -1 ) ^ 4 * ( z^-2))

f ' (z) = 5 ( 1 - z^ -1 ) ^ 4 / ( z^2)

f ' (z) = 5 ( 1 - 1/z ) ^4 / z^2