For the following exercises, given y = f(u) and u = g(x), find dy by using Leibniz's notation dx for the chain rule: dy %3D dy du dx du dx 1. y = 3u – 6, u = 2x2

Q: d?y Calculate y = e-(x - 9) – x d?y dx2 II

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Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: Evaluate cex-y) dx + C (x+3Y) dy C:xaxis from (0,0) to (0,-3) and 0-3) to (5,-3).

A: To Evaluate: ∫C2x-ydx+x+3ydyC: x-axis from 0,0 to 0,-3 and 0,-3 to 5,-3.

Q: In question (c), please use the computed result to explain why Dx=c is inconsistent

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Q: Use the chain rule. If y = √u and u = x2 + 11, find dy dx 11 dy dx

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Q: Find dy/dx for the function. x2 + 8x + y2 – 7y + 1 = 0 dy dx

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Q: Find dy/dx for the function. x² + 5x + y² – 9y + 1 = 0 dy 2х + 5 dx 2у — 9 II

A: Given: x2+5x+y2-9y+1=0

Q: (x² + y²)dy dx 7.

A: Given  ∫-22∫04-x2(x2+y2) dydx

Q: Find dy du du dx dy when y and u are defined as follows. dx u = 3x - 9x² and y = √u

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Q: Use the chain rule  If Y= 1/w and W= 3x-5, find dy/dx

A: First of all, consider the given substitution for y.Differentiate y w.r.t x and apply the chain…

Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: Find for y=x cott²dt. dy dx 2

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Q: Calculate dx y = x2

A: ddxxn=n xn-1