Calculus grade 12
a) determine the derivative of y = sin2x
b) determine the derivative of y = 2SinxCosx
c) shoe that derivatives in parts a) and b) are equal
d) explain why derivatives in parts a) and be should be equal.
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Answers
a) dy/dx = 2cos(2x)sin(2x) b) dy/dx = 2cos(2x)sin(2x) c) 2cos(2x)sin(2x) = 2cos(2x)sin(2x) d) The derivatives of y = sin2x and y = 2sinxcosx should be equal because both equations are equivalent formulations of the same function. In other words, both equations represent the same curve on a graph. Therefore, their derivatives must be the same.
