Q1

If x2 + y? = 1, find y'. y' =Find dy/dt using the given values. xy = 2 for x = 4,dx/dt = -2 dy dtAssume that x and y are differentiable functions of t. For the following, find dx/dt given that x = 6, y = 11, and dy/dt = 4. x2 + y2 = 157 dx dtThis question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 12, and dz/dt = 4. Step 1 To find - dy dt , start by differentiating both sides of the equation implicitly with respect to t. - ( x 2 + 12 ) = -" (2 2 ) 2x . . dx dy dz dt dt dt Submit Skip (you cannot come back)This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise The supply function for a product is given by p = 30 + 100 2x + 21, where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when the price per unit is $930? Step 1 The relationship between price p in dollars and the number of units x is given by p = 30 + 100 \\ 2x + 21. Rewrite the supply function in exponential form. p = 30 + 100 \\ 2x + 21 P = 30 + 100(2x + 21) If the price is increasing at a rate of $1 per month, this is a rate of change of price p with respect to time t and ---Select--- @) = 1. The unknown is the rate at which the supply is changing when the price per unit is $930. This is a rate of change of x with respect to time t or ---Select--- O . Submit Skip (you cannot come back)Suppose that for a particular product, the number of units x produced per month depends on the number of thousands of dollars y invested, with x = 60y + 40y". At what rate will production increase if $10,000 is invested and if the investment capital is increasing at a rate of $1000 per month? units/month2