Final answer:
To find the derivative of 5cos²(πx), use differentiation and the chain rule. The derivative is -10πcos(πx)sin(πx).
Step-by-step explanation:
To find the derivative of 5cos²(πx), we can use differentiation. The derivative of cos²(πx) can be found using the chain rule, which states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).
In this case, f(u) = u² and g(x) = cos(πx). So, f'(u) = 2u and g'(x) = -πsin(πx).
Therefore, the derivative of 5cos²(πx) is: dy/dx = 2 * 5 * cos(πx) * (-πsin(πx)) = -10πcos(πx)sin(πx).