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

adOrmaPem6r

adOrmaPem6r

Answered question

2021-12-01

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

Answer & Explanation

Harr1957

Harr1957

Beginner2021-12-02Added 18 answers

Use the Quotient Rule: (uv)=uvuvv2.
Note: It's given that f(5)=1, f'(5)=6, g(5)=-3 and g'(5)=2.
(gf)(5)=g(5)f(5)g(5)f(5)(f(5))2=2(1)(3)(6)12=201=20
Result:
20
RizerMix

RizerMix

Expert2023-05-12Added 656 answers

To find the value of (g/f)(5), we need to calculate the derivative of the quotient g(x)f(x) and evaluate it at x=5.
Let's begin by using the quotient rule to find (g/f)(x). The quotient rule states that for functions u(x) and v(x), the derivative of their quotient is given by:
(uv)(x)=u(x)v(x)u(x)v(x)v2(x)
In our case, we have u(x)=g(x) and v(x)=f(x). Differentiating these functions, we find:
u(x)=g(x)andv(x)=f(x)
Substituting these values into the quotient rule formula, we get:
(gf)(x)=g(x)f(x)g(x)f(x)f2(x)
Now, let's evaluate this expression at x=5 using the given values:
(gf)(5)=g(5)f(5)g(5)f(5)f2(5)
Substituting the provided values, we have:
(gf)(5)=2·1(3)·612
Simplifying the expression further:
(gf)(5)=2+181=201=20
Therefore, (g/f)(5)=20.
Vasquez

Vasquez

Expert2023-05-12Added 669 answers

Answer: 20
Explanation:
To find (g/f)(5), we can use the quotient rule. The quotient rule states that for two functions u(x) and v(x), the derivative of their quotient w(x)=u(x)v(x) is given by:
w(x)=u(x)v(x)u(x)v(x)(v(x))2.
In this case, u(x)=g(x) and v(x)=f(x). Let's differentiate u(x) and v(x) using the given information:
u(5)=g(5)=2,
v(5)=f(5)=6.
Now, let's substitute these values into the quotient rule formula and evaluate it at x=5:
(g/f)(5)=u(5)v(5)u(5)v(5)(v(5))2=2f(5)g(5)f(5)(f(5))2.
Substituting the given values:
(g/f)(5)=2·1(3)·6(1)2=2+181=201=20.
Therefore, (g/f)(5)=20.
user_27qwe

user_27qwe

Skilled2023-05-12Added 375 answers

The expression for the derivative of gf is:
(gf)=gffgf2
Thus, the value of (gf) at x=5 is:
(gf)(5)=g(5)f(5)f(5)g(5)f2(5)
Substituting the given values:
(gf)(5)=(2)(1)(6)(3)(1)2
Simplifying:
(gf)(5)=201
Therefore, (gf)(5) equals 20.

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