A curve has the equation y=sin(x)cos(x), find the gradient of this curve when x = pi. (4 marks)
Option 1 - Differentiate using product rule giving dy/dx = cos2(x) - sin2(x). (2 marks) Subbing in x as pi (1 mark) then gives (-1)2 + (0)2 . Therefore the gradient is 1 (1 mark). Option 2 - Initially changing sin(x)cos(x) into (sin2x)/2 (1 mark) using double angle identities, then using the chain rule to differentiate to cos(2x) (2 marks), finally subbing in x = pi for the answer of 1 (1 mark).
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