First the pieces: dz dx 8z dy da dt dy dt Use the chain rule to find dz dt || || || End result (in terms of just t): dz dt where 2 = x²y + xy², x = 3 + t², y = −2+t³

Q: Use the Chain Rule to find dw/dt. W w = xey/z, x = t5, y = 9 - t, z = 2 + 9t

A: w=xeyz , x=t5 , y=9-t , z=2+9tTo find : Fins the derivative dwdt using the chain rule.

Q: Use the Chain Rule to find dw/dt. dw dt || w = xeylz, xey/z, x=t5, y = 9-t, z = 2 + 9t X

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Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: dy Find if y= dt dy dt 11 1 2 u²+u and u = 4 + 5t.

A: The given function  and

Q: dy If y (t+ 2t + 6) (7t + 6), r find dt dy dt

A: Given  y=t2+2t+67t2+6y=7t4+6t2+14t3+12t+42t2+36y=7t4+14t3+48t2+12t+36

Q: Find dt y = 6t + /9+ 7-t dy dt |3|

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Q: - given that 2 = 2x + 4y, x = 3 y = 1, and dx dt = 6

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Q: dy If y = (t + 2t + 5) (7Ł² + 3), find dt dy dt

A:

Q: Let x(t) = 3-3t, y(t) = 3t+1. Find dy/dx

A: First, we need to find the derivative of x(t) with respect to t. The derivative of a function…

Q: dx 5 x + 2y 2 dt dy 3 ーX 4 – 2y dt

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Q: Find dy dr || - for y = dr r S 9 +10t2 dt. 0

A: To find dydr for y=∫0r9+10t2 dt.

Q: If fo f(t)dt = 2, So f(t)dt = -6, and f(t)dt = 1, find i f(t)dt.

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Q: = xy³ + x2y, x = 31- 8, y = 4t2 - 4. dw when t 1. dt Use the Chain Rule to calculate dw dt

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

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Q: dy If y = (t² + 7t + 5) (2t² + 6), find dt

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Q: dy If y = (t + 6t + 5) (6t² + 6), find dt dy dt ||

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