Problems 1& 2 involve three functions z(y), y(u), and u(x). Find dz/dx from (dz/dy)(dy/du)(du/dx). 1. 1= /sin(x -+ 1} 2. z= (sin x')?

Q: 2. One of (a)-(c) is incorrect. Find and correct the mistake. (a) - sin(y³) = 2y cos(y?) (b) dx…

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Q: 4. S sinºx dx

A: This question can be solved by applying the concepts of integration of trigonometric functions.

Q: 3. Let x² + 4xy + y² = 13. dy • Find dx by using implicit differentiation.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 6. S 2sin´x sin(2x) dx

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Q: 21. y = sin xy

A: y= sin xydydx=ddxsin xy       =cos xyddxxy       =cos xyxdydx+yddxx       =cos xyxdydx+y       =x…

Q: 5y + sin y = x²

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Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: 8. Find y'if y = x³ +sin (x)

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Q: 8) Given the function y =x – 3x+1 dy Find the derivative, dx

A: Solve by derivative of given function

Q: Differentiate the following function. y= cos 14x

A: We will find the solution in the following step

Q: 4. ſ cos xesinx dx

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Q: Let y = sin (x + y), find y'.

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Q: 7. Find y'if y=x³+ sin (x)

A: given

Q: 2. Find dy/dx: a. 3x? – (xy²)½ = 2y³ b. у%3D (сosx — ях)4x*

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Q: 6. x cos x, find the second derivative. 7. y = sin? x, find y dx2 d²y 8. y = tan(3x²), find · dx2"

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Q: 2. Find the derivative of the function. y = e* In (sinæ)

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Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: I ind the second derivative(y") of the following functions and simplify the final results. 1. y = x…

A: Differentiate using the rules of derivative.

Q: hind dy if y = sin(x")

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Q: 3 5. y= 23x+1 %3D 2 3x+1

A: Given : y = 323x + 1