First principles: reciprocal function

A question is this type if and only if it asks students to differentiate 1/x or a similar reciprocal function from first principles.

1 questions · Standard +0.3

1.07g Differentiation from first principles: for small positive integer powers of x
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Pre-U Pre-U 9794/1 2013 June Q12
6 marks Standard +0.3
12
  1. Prove the identity \(\frac { 1 } { ( x + h ) ^ { 2 } } - \frac { 1 } { x ^ { 2 } } \equiv \frac { - 2 h x - h ^ { 2 } } { x ^ { 2 } ( x + h ) ^ { 2 } }\).
  2. Given that \(\mathrm { f } ( x ) = x ^ { - 2 }\), use differentiation from first principles to find an expression for \(\mathrm { f } ^ { \prime } ( x )\).