• ƒ(•) : R² → R² and g(-) : R³ → R² are given by ƒ (») = (37,³² (1²1/2-1/²) 3y₁ + y₂ Find the Jacobians ƒ'(y) and g'(x). For x = (−1 2 1)¹, find g′(§), ƒ' (g(x)), and (ƒog)'(X). Suppose X1 and gx₂= x3 x₁ + x₂ + x3 √x²x₂x3 + x²³

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A: We have to find

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A: Given a differential equation:initial conditions are:

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A:

Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: Use the crossing-graphs method to solve the given equation. (Round your answer to two decimal…

A: crossing graph method is suitable for equations having a higher degree. In this method left hand and…

Q: Find G′(w) if G(w)=5/ 9w^5 +7 sqaure root w. G'(w)

A:

Q: y=f(x)=x' - 4x +10 find the interval that f(x) graph is concave down. O A) (2, infinite) O B) (0, 3)…

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Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

Q: (a) y'=ty (3-y), (b) y'=y (3-ty), (c) y'= -y (3-ty), (d) y'=t-1-y², y(0) = yo y(0) = yo y(0) = yo…

A: We will be graphing the slope field of the given differential equation along with the interpretation…

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

A:

Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

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)·…

A:

Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

A:

Q: Let F(2) = f(x) and G(x) = (f(x)) - You also know that a = 2, f(a) = 2, f'(a) = 7, f'(a³) = 15. Find…

A:

Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

A:

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

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A:

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A:

Q: Suppose that ♬ = 5x²/5 + ev/²3, and let C be the path consisting of (i) an arc along y = x² - 1 from…

A:

Q: Find y as a function of x if y" + 16y' = 0, y(0) = 0, y'(0) = 4, y'(0) = -32. y(x) =

A:

Q: Find y' (x) if (3xy +7)² = 6y.

A: Differentiate both sides with respect to x and by using the formula for derivative of square of…

Q: Given the function, Show that it is not continuous at (3,-1) and determine the slope of the line…

A: The function will be discontinuous at 3, -1, if  either f(3,-1) is not defined, or,…

Q: (2xy + 3x²)e +(x² – 2yz + 2y)e,y- (e² + y²)e, olan f(x, y,z)

A: Given