# Calculus

How do you find the derivative of (x-2)^.5 times (2x+1) times (x-3)^-.666666667? What is the final answer as well?

1. 👍
2. 👎
3. 👁
1. I see

y = (2x+1)(x-2)^.5 / [(x-3)^(2/3)]

There are many ways to do this to find dy/dx

one is to use the quotient rule and just slug it out.

If you know logs, there is a nice way:

using the rules of logs we get

ln y = (1/2)ln(x-2) + ln(2x+1) - (2/3)ln(x-3)

then (dy/dx) / y = 1/(2(x-2)) + 2/(2x+1) - 2/[3(x-3)]

multiply both sides by y, replacing y with the orignal function on the right side, and you have dy/dx

1. 👍
2. 👎

## Similar Questions

1. ### math

Which comparison sentence best represents the equation? 6x7=42 7 is 6 times as many as 42. 6 is 7 times as many as 42 or 42 is 6 times as many as 7.

2. ### Biology

if the surface area of a cell that is shaped like a cube increases 100 times, it’s volume increases about… A. 5 times B. 10 times C. 100 times D. 1000 times.

3. ### Physics

If a ball is thrown directly upwards with twice the initial speed of another, how much higher will it be at its apex? A) 8 times D) 2 times B) 4 times E) 2 times C) 2 2 times Please show any equations that are used :)

4. ### Math - Derivative of a polynomial function

The population, p in thousands of bacteria colony can be modelled by the function p(t)=200+20t-t^2, where t is the time, in hours, t is greater than or equal to zero. a) Determine the growth rate of the bacteria population at each

1. ### calculus

The decibel level of a sound is given by the equation D=10log 10 (i/i 0), where "i" is the sound's intensity and "i 0" corresponds to the intensity of the weakest sound that can be detected by the human ear. Approximately how many

2. ### Chemistry

for each of the following, give an answer with the correct number of significant figures: A. 400 times 185 b. 2.40 divided by 4 times 125 c. 0.825 times 3.6 times 5.1 d. 3.5 times 0.261 divided by 8.24 times 20.0

3. ### math

Haley’s work evaluating (Negative 2) Superscript 8 is shown below. (Negative 2) Superscript 8 = (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) = negative 256 Which

4. ### Calculus

Find the area of one petal of the polar curve r = 3 cos 3θ. (4 points) A) 7 times pi over 12 B) 3 times pi over 4 C) 11 times pi over 12 D) 2π

*I NEED THESE IN ALGEBRAIC EXPRESSIONS! 1.) The larger of two numbers is 1 less than 3 times the smaller. Their sum is 63. Find the numbers. 2.) Find two numbers whose sum is 92, if the first is 4 more than 7 times the second. 3.)

2. ### Algebra

Seven times the smaller of 2 numbers plus 9 times the larger is 178. When 10 times the larger is increased by 11 times the smaller the result is 230. Find the numbers.

3. ### Math

If you toss a pair of dice 1,000 times, how many times would you expect to get a sum of 12 as the result? 1.)about 12 times 2.)about 27 times 3.)about 36 times 4.)about 100 times The lesson doesn't show me how to work this. Whats

4. ### math question

/how do i solve this? The probability of winning a game is 15%. If you play 20 times,how many times should you expect to win? A.5 times B.3 times C.6 times D.15 times