If a function y(x) can be expressed as the ratio cg(x) + G(x) cf(x) + F(x) y = where c is a constant and g, G, ƒ and F are differentiable functions of x, by eliminating the constant c from this equation and its first derivative, show that y satisfies a Riccati equation.

Q: a) If a derivative of the function is given as: f'(x) = 9x² + 16x - 7 i) Find the function f(x) in…

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Q: 2. Find the derivative of f'(x) if ƒ(x) = x*+3x-V x2+x

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Q: Find the derivative of the following functions a) f(x) = 1 + x² + = 160 1x x6 I b) F(X) x4-3x+1 √x…

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Q: a) Find an equation of the tangent line to the curve. y=f(x)3x2-4x at x = 2. b) Find the derivative…

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Q: The derivative of f(x) = In(5x³ – 12) Is

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Q: In another universe, there are some extra functions that their mathematicians use: stars, sun and…

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Q: a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent…

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Q: 1. Find the derivative of the following: a) 3x²+6x f(x)= 5x-1

A: according to bartleby guide line we do only first part of multiple questions…

Q: 8) Find the derivative of the function f(x) = (2x-1 x² + 1 if x ≤0 if x>0

A: Step 1:   Step 2: Step 3: Step 4:

Q: In 1994, the moose population in a park was measured to be 3540. By 1999, the population was…

A: Formula , slope of line  m = ( y2 - y1 ) / ( x2 - x1 )

Q: Explain why the derivative of a 2x – 3 is two, i.e. if f(x) = 2x – 3, then f’(x) = 2. Use proper…

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Q: (b) g(x):= 1/x for x E R, x#0, (d) k(x):= 1//x for x > 0.

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Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: the product rule is not needed to find the derivative of y = 3(x² – 2). the quotient rule is[not…

A: Product rule: If we are given a function of the form: f(x)·g(x), we can find the derivative of this…