01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

Q: dy 3YUse implicit differentiation to find y or a) 2x +v° =7x² -6 b) x +xy=y +15

A:

Q: Find əw/ar and aw/as when r = n and s = 0 if w = sin(2x – y), x = r + sin s, y = rs.

A:

Q: of

A:

Q: f(x)=x+5 glx)=x -1

A:

Q: 2. J Зу /7—Зу?dy

A:

Q: What is the value of t in terms r, s, and u In the equation

A: The solution is easy to see

Q: Q4. Let fla) < cos" ( a ) Find fCa) COS n+5 f'(a) = %3D

A: Answer is mentioned below

Q: Consider the following. u = (2, 0), v = (5, 7) (a) Find u · v. U'V = (b) Find the angle between u…

A: Given that  The vectors  u=(2,0) and v=(5,7) To find the u.v and angle between the u and v

Q: If g(r,s,t) = et sin(st), find dsdr2*

A: Given Data: Function: gr, s, t=ertsinst   The triple partial derivative can be rewritten as,…

Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

A:

Q: Find the derivative of y. 30) y- In (sinh 9x) 1. B) sinh 9x A) coth 9x C) 9 csch 9x D) 9 coth 9x

A: Derivative

Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

A:

Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

A:

Q: dw 21. : 1-cosw A. -tan w + secw + C B. w – cotw + C C.-cotw – cscw + C_ D. -cscw + tanw + C

A: We can find the integral value as below.

Q: -1

A: Given,

Q: Show that (∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

A: The equation to be proved is,