For $y=\frac{3x+5}{x-3}$ , find the instantaneous rate of change when x=2

Ernstfalld
2021-09-19
Answered

For $y=\frac{3x+5}{x-3}$ , find the instantaneous rate of change when x=2

You can still ask an expert for help

Anonym

Answered 2021-09-20
Author has **108** answers

Step 1

$y=\frac{3x+5}{x-3}$

$\frac{dy}{dx}=\frac{(x-3)\frac{d}{dx}(3x+5)-(3x+5)\frac{d}{dx}(x-3)}{{(x-3)}^{2}}$

Step 2

$\frac{dy}{dx}=\frac{(x-3)3-(3x+5)}{{(x-3)}^{2}}$

$\frac{dy}{dx}=\frac{3x-9-3x-5}{{(x-3)}^{2}}$

$\frac{dy}{dx}=\frac{-14}{{(x-3)}^{2}}$

$\left(\frac{dy}{dx}\right)}_{x=2}=\frac{-14}{{(2-3)}^{2}$

${\left(\frac{dy}{dx}\right)}_{x=2}=-14$

So instantaneous rate of change =-14

Step 2

So instantaneous rate of change =-14

asked 2021-05-23

Use the given graph to estimate the value of each derivative.(Round all answers to one decimal place.)Graph uploaded below.

(a) f ' (0)1

(b) f ' (1)2

(c) f ' (2)3

(d) f ' (3)4

(e) f ' (4)5

(f) f ' (5)6

(a) f ' (0)1

(b) f ' (1)2

(c) f ' (2)3

(d) f ' (3)4

(e) f ' (4)5

(f) f ' (5)6

asked 2021-03-07

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? Give examples.

asked 2021-10-14

Find the first and second derivatives: y = 1x + 1

asked 2021-02-27

Find all first partial derivatives. $f(x,y)={y}^{3}{e}^{\frac{y}{x}}$

asked 2022-05-12

If $f(x)=\mathrm{sin}(\frac{\pi x}{3})$ and $g(x)=4{x}^{3}+2$, what is f(g(x))'?

asked 2022-03-25

Calculating derivatives Find dy>dx for the following functions.

$y=\frac{\mathrm{sin}x}{1+\mathrm{cos}x}$

asked 2022-08-18

Find the indicated partial derivative. $f(x,y,z)=\frac{y}{x}+y+z;{f}_{y}(2,1,-1)$