Differentiate y = 7(x)^2 + cos(x)sin(x)

This question uses a combination of standard differentiation and the product rule. The second part of the equation cos(x)sin(x) is the product of two funtions so the product rule must be used. Product rule: (fg)'(x) = f '(x)g(x) + f(x)g'(x) Let f(x) = cos(x) and g(x) = sin(x). The differentials are: f'(x) = -sin(x) and g'(x) = cos(x)

Differentiating the equation you get dy/dx = 14x + -sin(x)sin(x) + cos(x)cos(x)  dy/dx = 14x + cos^2(x) - sin^2(x) The equation is now differentated but can be simplified by using the identity cos(2x) = cos^2(x) - sin^2(x) The final answer is therfore: dy/dx = 14x + cos(2x)