Differentiation - Application
Hello! I would be incredibly thankful if somebody could show step by step how they solve this question:
A new car hire company has just opened and wants to make the maximum amount of profit. The amount of profit, P, is dependent on two factors; x, the number of tens of cars rented; and y, the distance travelled by each car. The profit is given by the formula: P=xy+40, where y=sinx. Find the smallest number of cars that the comapny needs to rent to give the maximum amount of profit.
This is how i've done it so far:
P = xy+40
P = x*sinx+40
dp/dx=sinx+xcosx (product rule)
sinx+xcosx = 0
My answer is obviously wrong, so I'd appreciate some help!