find (f+g)' (2), h'(1) when h(x) = f(x)g(x), and h'(1) when h(x) = f(x) / g(x)

Q: A1) Using the definition of derivative, find the derivative of f(x) = x² + 7x + 7.

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Q: he first principle to determine f'(x) of the following functions: f(x)=x2 f(x)=x2-

A: f(x) = x2 ddx(f) = f'(x) = 2x

Q: Let f(x) = (2x-3)/(x-1) as x --> - infinity,    f(x) --> ?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Q3/ find the derivative D f(x) = x log5 @f(x) = (x+3) ² 2x+4 2 X

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Q: f(x)=(8x-1)(x2+4x+7)(x3-5) find the derivatives

A: fx=8x-1x2+4x+7x3-5 On simplification, we get…

Q: Consider the following function. f(x) = x* - 16x3 + 72x2 + 2 (a) Make a sign diagram for the first…

A: Using first derivative test.

Q: What happens to the values of f(x)=(x2-2x-3)/(x2-3x) as x ->0 ?

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Q: find the derivative of f(x) = (x² +4)(3x³-2x) at the point x =- 3[use product rule]

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Q: Find f'(x) in two ways: (1) using the product rule and (2) simplifying first. f(x)=x²(x²-5) Which of…

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Q: What rule do you use to calculate the derivative of f(x) = exx2 and f(x)=(x2-3x+1)/(x+5) ?

A: Use the product rule and quotient rule of derivative: