Let U = {1,2,3,4,5,6,7,8,9); X= {2,4,6,8}; Y={2,3,4,5,6}; Z={1,2,3,8,9} XnY X' Yn(XuZ) (XnY') u (Z'nY') X'nZ X’n(Y’uZ) (XnY) u (X'nZ)

Q: Let F(z) = f(cos(x)) · sin (금) and G(x) = f(sin(x)) · cos : (주) and suppose that f(0) = 5, f(1) =…

A: We have to find

Q: ■ If y = Σº。 (k + 1) x²+³ then y² = 0 k=0 k=0

A: The function is given by y = ∑k=0∞k+1xk+3 To determine: The first derivative of the function.

Q: 2. Let u,v be functions of x. The first order derivative of uv can be derived by the following…

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Q: A table of values for f,9, f', and g' is given below: z f(z) g(z) | f'(z) g'(z) 1 3 2 4 6 2 1 8. 7 3…

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Q: If gw + xcos tgcx) = x7, find gro) g'co) =

A: We have to find

Q: S(c^~q) S→(-avr) a p

A:

Q: 3) u = y f( ise XU, + yu, t zu. = ?

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Q: Let g(s) = (282)7. Then g'(s) is g'(2) is g" (s) is and g' (2) is "

A: Solving the following problem

Q: Let g(s) = (5s – 8)*. - Then g'(s) is g'(3) is s! (s),,6 and g''(3) is

A:

Q: Find a function y(æ) such that byy' = x and y(6) = 5. y =

A: y' = dy/dx y(6) = 5 means at x=6 => y=5

Q: If y = (x+-) (2x – 3), then dy will be dx a (2x+) + (x = 3)(1 +) G++)(e - x2) + (; ++) = A. (2x +=)…

A: Given that                          y=x+1x2x-3

Q: Jige If f(2) =-3, g(2) =4, f' (2) =2, and g' (2) =, d. then dx -21 16 9. 16 -13 16 29 16 6 jp 3…

A:

Q: A table of values for f, g, f', and g is given below. xf(x) g(x) f'(x) g(x) 1 2 3 2 3 1 3 1 3 3 1 3…

A: (A) The derivative h'x can be represented as follows: h'x=f'gx·g'x

Q: Find y,(x) if y = In(In(Inx)).

A:

Q: 4. If /(r.y)=- , find f, and f,. V+y

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Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

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Q: If p(E) = 2 9, find o(E) and o(E'). o(E) =       o(E') =

A: Given p(E)=29=n(E)n(S) That is, n(E)=2 n(S)=9 n(S)=9n(E)+n(E,)=92+n(E')=9     n(E')=7

Q: 12. Let f(z,y) = < then f(1,2) = (b) 글 (d) 금

A: Given :fx, y=x-yx+y-1

Q: 6) When some variable z is a function of time (t), the derivative of z with respect to t is denoted…

A:

Q: Let g(x) = 2 f(u) + 3 where . u= u = with respect to x? ○ 2. f' (u) +3 O (2. f' (u) + 3) (2x + 2)…

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Q: Which among the choices is different from the others? (G' o h')(t) G'(h(t))h'(t) O (G' • h)(t)h'(t)…

A: We have to find the different form  others

Q: - Find V x+y `

A: Given that, fx,y=x+yx-y We have to find ∇f. We know that, ∇f=∇x+yx-y=∂f∂x,∂f∂y

Q: Let f(x) = 5x² cos(2x). f'(x) = -10x²(2x) + 10x cos(2x) f'(5) = 0 f"(x) = -10x² sin (2x) + 10x…

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Q: Let F(#) f(/(=)) and G(r) =(F(2))2 and suppose that f(5) = 6, f(6) = 3, f'(6) = 7, f'(5) = 15 Find…

A:

Q: In (z z2) =

A: I have provided this answer in step-2.