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

(1)Rewrite the function as a quotient.(fg)(x)=f(x)g(x)(2)Find the derivative using the quotient rule.(fg)′(x)=f′(x)g(x)−f(x)g′(x)[g(x)]2(3)Substitute x=5.(fg)′(5)=f′(5)g(5)−f(5)g′(5)[g(5)]2Substitute f'(5)=3, g(5)=-6, f(5)=2, and g'(5)=1.=3(−6)−2(1)(−6)2(5)Simplify=−2036(6)Reduce the fraction.=−59

Expert answers to "Suppose that f(5) = 2, f'(5) = 3,..."

saborcehj

Open question

2022-08-17

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

Answer & Explanation

lywyk0

Beginner2022-08-18Added 12 answers

(1)Rewrite the function as a quotient.

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

(2)Find the derivative using the quotient rule.

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

(3)Substitute x=5.

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

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

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

(5)Simplify

= \frac{- 20}{36}

(6)Reduce the fraction.

= - \frac{5}{9}

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of $9 x^{2} + 16 y^{2} = 144$ ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle $x^{2} - 12 x + y^{2} + 4 y + 15 = 0$ ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III
How to find the center and radius of the circle given $x^{2} + y^{2} + 8 x - 6 y = 0$ ?
How to find the center and radius of the circle $x^{2} + y^{2} + 4 x - 8 y + 4 = 0$ ?
How to identify the center and radius of the circle ${(x + 3)}^{2} + {(y - 8)}^{2} = 16$ ?

Didn't find what you were looking for?