Suppose that f(5) = 2, f'(5) = 3, g(5) = -6, and g'(5) = 1. Find the following values:(g/f)'(5)

(1)Rewrite the function as a quotient.(gf)(x)=g(x)f(x)(2)Find the derivative using the quotient rule.(gf)′(x)=g′(x)f(x)−g(x)f′(x)[f(x)]2(3)Substitute x=5.(gf)′(5)=g′(5)f(5)−g(5)f′(5)[f(5)]2(4)Substitute f'(5)=3, g(5)=-6, f(5)=2, and g'(5)=1.=1(2)−(−6)(3)22(5)Simplify.=204(6)Reduce the fraction.=5

Question: "Suppose that f(5) = 2, f'(5) = 3,..."

Fortura7i

Open question

2022-08-19

Suppose that f(5) = 2, f'(5) = 3, g(5) = -6, and g'(5) = 1. Find the following values:
(g/f)'(5)

Answer & Explanation

Adam Bradley

Beginner2022-08-20Added 10 answers

(1)Rewrite the function as a quotient.

(\frac{g}{f}) (x) = \frac{g (x)}{f (x)}

(2)Find the derivative using the quotient rule.

{(\frac{g}{f})}^{'} (x) = \frac{g^{'} (x) f (x) - g (x) f^{'} (x)}{{[f (x)]}^{2}}

(3)Substitute x=5.

{(\frac{g}{f})}^{'} (5) = {\frac{g^{'} (5) f (5) - g (5) f^{'} (5)}{[f (5)]}}^{2}

(4)Substitute f'(5)=3, g(5)=-6, f(5)=2, and g'(5)=1.

= \frac{1 (2) - (- 6) (3)}{2^{2}}

(5)Simplify.

= \frac{20}{4}

(6)Reduce the fraction.
=5

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