Let z(x, y) = x³y where x = Calculate da dt = t³ & y = 1⁹. = dz dx dy by first finding & and using the chain rule. dt dt dt dy dt Now use the chain rule to calculate the following:

Q: Find dy/dt.

A: Given, y=9-4x3+2x; dxdt=-1,x=-3 To find dydt

Q: If y = 2x3 + 5x and dx = 2, find dt dy Y when x = 4. dt dy - dt

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Q: secx 1 Given g(x) : z dt , find g'(x). t2

A: gx = ∫7sexcx1t2dt           = ∫7sexcx t-2 dt        = t-2+1-2+7secx      =t-17secx-1 = secx-1-7-1-1…

Q: Find dx dt da dt at x = 5 if y=-x² - 1 and dy dt 1.

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Q: dy = 3. dt dx at x = 4 if y = - 2x² + 5 and dt Find dx dt

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Q: Given t = x + ex, find dx/dt

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Q: which is f-1 (x)? f(x)= 1/5x + 3/5

A: Given, fx=15x+35 We have to find f-1x.

Q: Let dx dt x(t): = 3et 2. Find x(t) such that x(0) = 2.

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Q: dx Assume that x= x(t) and y = y(t). Let y = x³ +5 and dt=4 when x = 1. Find dt 11 dy when x = 1.…

A: The objective of the question is to find the rate of change of y with respect to time (dy/dt) when x…