Derivatives: The question is y= (4x^2 -5)^-3/2(2-3x)^4

[thelazyman]

Hi, the question is

y= (4x^2 -5)^-3/2(2-3x)^4

I got to this step

-12(2-3x)^3(4x^2 -5)^-5/2 ((2-3x)(4x^2-5)^-1)

 

[stapel]

Hi, the question is y= (4x^2 -5)^-3/2(2-3x)^4

Unfortunately, this is just an equation; there is no actual question here. Are you supposed to graph, using max/min information from the derivative? Are you supposed to find critical points? Inflection points? Intervals of increase or decrease? Or something else?

Also, your formatting is ambiguous. Do you mean any of the following?

. . . . .\(\displaystyle \L y\, =\, \frac{4x^2\, -\, 5)^{-3}}{2(2\, -\, 3x)^4}\)

. . . . .\(\displaystyle \L y\, =\, \left(4x^2\, -\, 5\right)^{\, \left(\frac{-3}{2(2\, -\, 3x)^4}\right)}\)

. . . . .\(\displaystyle \L y\, =\, \left(4x^2\, -\, 5\right)^{-\frac{3}{2}}\, \left(2\, -\, 3x\right)^4\)

Or did you mean something else?

I got to this step

-12(2-3x)^3(4x^2 -5)^-5/2 ((2-3x)(4x^2-5)^-1)

How?

Please reply showing all of your work and reasoning. Thank you.

Eliz.

 

[thelazyman]

Need to simplify fully


The actual question is:


(4x^2 - 5)to the power of -3/2 (2-3x)to the power of 4

 

[stapel]

Need to simplify fully

You need to simplify what fully? The original function? The second derivative? Or something else? Please provide the full text of and instructions for the exercise.

The actual question is:

(4x^2 - 5)to the power of -3/2 (2-3x)to the power of 4

Is that the third option I'd listed previously? (You didn't say "the third one you posted", which implies that we're still not understanding what you mean, is why I ask.)

When you reply, please include a full listing of all of your work and reasoning so far. Thank you.

Eliz.