Final answer:
To find an expression for dπ/dQ, we use the product rule to differentiate the function π(Q). Similarly, to find an expression for dπ/dL, we use the product rule to differentiate the function π(L).
Step-by-step explanation:
To find an expression for dπ/dQ, we need to take the derivative of the function π(Q) with respect to Q. Given that π(Q) = QP(Q) - cQ, where P is a differentiable function and c is a constant, let's find the derivative.
Using the product rule, we differentiate the first term QP(Q) and the second term -cQ separately. The derivative of the first term is Q * dP/dQ + P(Q) and the derivative of the second term is -c.
Combining the derivatives, we get dπ/dQ = Q * dP/dQ + P(Q) - c.
Similarly, for part b), to find an expression for dπ/dL, we need to take the derivative of the function π(L) with respect to L. Given that π(L) = PF(L) - wL, where F is a differentiable function and P and w are constants, we can differentiate the first term PF(L) and the second term -wL separately using the product rule.
The derivative of the first term is P * dF/dL + F(L) and the derivative of the second term is -w.
Combining the derivatives, we get dπ/dL = P * dF/dL + F(L) - w.