Let the fame tional J[y] = {² (y² + yy") dx, and the boun dary condition are y (x₂)=0 sy(x₂) = x₁, y'(x)=y!! y'(x) = X ₁"

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Q: The first derivative of a continuous function y=f(x) is given. Find y' and then sketch the general…

A: The first derivative of a continuous function y=f(x) is given.

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Q: 1. Find the derivative f'(z) if it exists, and state where f(z) is analytic. *(i) ƒ(z) = (1 − 3z²)4.…

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Q: 19 Let u(x) = sin(x) and v(x) = x¹9 and f(x) = u'(x) = v'(x) = u'v - uv' f' 2² u(x) v(x)

A: sin(x)' = cos(x) dxndx=n.xn-1

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Q: Which of the following is true about the derivatives of differentiable functions f an d da (2) –…

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Q: 6.) What is the derivative of f(x) = x| at x= 07 a.) r'(x) = 1 c.) f'(x) = 0 b.) f'(x) is undefined…

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Q: dy y = f(g(x)) then dx b. f'(g(x))g'(x) fg'(x)+ g(x)f" f'(x)g'(x) c. f(x) с. e. none of these II

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Q: 4 Suppose that f(1) = 1, f(4) = 9, f'(1) = 5, f'(4) = 5, and f" is continuous. Find the value of *…

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Q: Find the derivative of y with respect to the appropriate variable → 49. y = cos '(x²) sin-'V2! 50. y…

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Q: A function y = f(x) is increasing at x = g if A. f"(a) = 0 B. f'(a) 0

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Q: The first derivative of a continuous function y = f(x) is given. Find y" and then sketch the general…

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