Show that if ƒ and g have continuous second derivatives and f(a) = g(a) = f(b) = g(b) = 0, then | s«g"(x)dx = | g(x)f"(x)dx.

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

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Q: If f(x) = x5(4x + 5)6, compute the first and second derivatives of f(x). f'(x) = f"(x) =

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Q: Find the derivative of f(x)) at x = 3 if f(3) = 2, g(3) = = 5, f'(3) = 7, and g'(3) = 4.

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Q: Let f(x) = (x² + 4x) (x³ + 6) . Find ƒ'(1). (Hint: First take the derivative to find f'(x). Then…

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Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find the function such that f'(x)  = f(x) (1- f(x)) and  f(0)  = 1/2

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Q: Suppose that f(a) = f(b) = g(a) = g(b) = 0 and the second derivatives of f and g are continuous on…

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Q: and assume f(-2) =0 f'(– 2) = - 1. Find h'(-2). Let h(x) =x²e*(x)

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Q: Let f(x) = 5 sec(5x) f'(x)

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Q: Let f be a function of x defined by ex f(x) + 15x-9x² =0. The derivative of f at x is f'(x) =

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Q: Suppose f(-3) = 3, f'(-3) = 5, = -8, and %3D g(-3) = 1, gʻ (-3) = H(x) = f(x)e®(x). Find the…

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Q: Find g'(4) given that f(4) = -1 , f'(4) = -2 , and g(x) = Vãƒ(x).

A: Use the product rule to find the derivative of the function:

Q: Find the derivative of h(x) = e³ + Vx + lnx. I

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Q: if f(x)=cosx-3tanx, then f′(x)= f'(5)=

A: The given function is f(x)=cosx-3tanx