If x= f(u, v), y = g(u, v), u = D(r,s), and v=Y(r,s) are differentiable functions then prove that (***)-(***) (*) = 24,

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A: our objective is to find the required derivative

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A: Rolle's theorem

Q: 3. Let f be continuous on [-1, 4] and differentiable on (-1,4). If f(-1) = –1 and f(4) = 4, then the…

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Q: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

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A: if we want to fine any fuction has relative extrema then

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Q: 1. Consider the function y = f(x) displayed below. y 3 это 5 (a) For which values of x in the open…

A: Let's analyze the function y = f(x) displayed in the graph and address each part of the question:(a)…

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Q: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

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Q: Suppose f(z) is defined on all of C, is differentiable at z = a, and satisfies f(a) = a. Show that…

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Q: If f" CQ) = xa (x+)S (x-!) And all inflection points.

A: I have appended the concept used in the solution part

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A: We need to find inverse function.

Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…