Can you please give me an answer to this question like so

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Tasya [4]

Answer:

$\frac{dy}{dx}=-[(\frac{5x+24}{36x-6x^2})]$

Step-by-step explanation:

Given function:

y = $\ln(\frac{(6 - x)^{\frac{3}{2}}}{x^{\frac{2}{3}}})$

we know

$\ln(\frac{A}{B})$ = ln(A) - ln(B)

thus,

y = $\ln((6 - x)^{\frac{3}{2}}) - \ln(x^{\frac{2}{3}})$

or

also,

ln(Aⁿ) = n × ln(A)

thus,

y = $(\frac{3}{2})\times\ln(6 - x) - (\frac{2}{3})\times\ln(x)$

therefore,

$\frac{dy}{dx}=[(\frac{3}{2})\times\frac{1}{(6-x)}\times(0 - 1)] - [ (\frac{2}{3})\times\frac{1}{x}\times1]$

or

$\frac{dy}{dx}=-(\frac{3}{2(6-x)}) - (\frac{2}{3x})$

or

$\frac{dy}{dx}=-[(\frac{3(3x)+2\times2(6-x)}{2(6-x)\times(3x)})]$

or

$\frac{dy}{dx}=-[(\frac{5x+24}{36x-6x^2})]$

5 0

3 years ago

What's the answer??? idk ......

Rom4ik [11]

Fin a common number all of the numbers shown have in common. Like multiply 7 x 5 x 6 and you get 210. and for .4 the simplified version of that in 2/5

3 0

2 years ago

Read 2 more answers

2 7/8 + 6 1/6 =?plzz i need help!

ella [17]

6 8/48 and 2 7/48 equal 8 15/48

7 0

2 years ago

Find the distance between each pair of points (6,-2) (8,-3)

alina1380 [7]

Answer:-1/2

Step-by-step explanation: You just find the slope which is m=y2-y1

-------

x2-x1

5 0

2 years ago

Read 2 more answers

Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC

Marysya12 [62]

BC is 10 units and AC is $5+5\sqrt{3}$ units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}$
AB is opposite to ∠C
BC is opposite to ∠A
AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∵ AB = $5\sqrt{2}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}$

- By using cross multiplication

∴ (BC) × sin(30) = $5\sqrt{2}$ × sin(45)

∵ sin(30) = 0.5 and sin(45) = $\frac{1}{\sqrt{2}}$

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ $\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}$

- By using cross multiplication

∴ (AC) × sin(30) = $5\sqrt{2}$ × sin(105)

∵ sin(105) = $\frac{\sqrt{6}+\sqrt{2}}{4}$

∴ 0.5 (AC) = $\frac{5+5\sqrt{3}}{2}$

- Divide both sides by 0.5

∴ AC = $5+5\sqrt{3}$ units

BC is 10 units and AC is $5+5\sqrt{3}$ units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0

3 years ago