1 Consider the function f(x) x 1 derivative (or by First Principles) we can get: =...

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1 Consider the function f(x) x² 1 derivative (or by First Principles) we can get: = x²-1-(x²2 + 2xh+h² - 1) h(x². - 1)(x² + 2xh+h² 1) (i) Write the first step of working that must have been done. [2 marks] (ii) From the equation given in the question, use algebraic techniques and the tool of the limit to give the derivative for f(x) [3 marks]. f'(x) = for {x R,x 1}. Using the definition of the lim h→0 Using First Principles, show that the derivative of h(x) = √x is h'(x) HINT: After the first step, think about rationalising the numerator. = 1 2√x [6 marks] 1 Consider the function f(x) x² 1 derivative (or by First Principles) we can get: = x²-1-(x²2 + 2xh+h² - 1) h(x². - 1)(x² + 2xh+h² 1) (i) Write the first step of working that must have been done. [2 marks] (ii) From the equation given in the question, use algebraic techniques and the tool of the limit to give the derivative for f(x) [3 marks]. f'(x) = for {x R,x 1}. Using the definition of the lim h→0 Using First Principles, show that the derivative of h(x) = √x is h'(x) HINT: After the first step, think about rationalising the numerator. = 1 2√x [6 marks]