differentiate f(x) = 4/x^2 - sqrt.x^3 + 1/ sqrt.x - 1

[yanarains]

Differentiate the given function and simplify your answer

f(x)= 4/x^2-sqrt.x^3+1/ sqrt.x - 1

(note that x^3 and x are under the radical sign, im not certain how that is shown)

f(x)= 4(-2x) - 3x^-1/2 +1/2x^-3/2
= -6x +3/2x^1/2 - 1/2x^-3/2

UMMMM>>>> could someone help this doesn't feel right. Like I have said before these radicals confuse me. Are my steps even close to correct?

Thank you for the help

 

[stapel]

Differentiate the given function and simplify your answer

f(x)= 4/x^2-sqrt.x^3+1/ sqrt.x - 1

(note that x^3 and x are under the radical sign, im not certain how that is shown)

You have two "divided by" slashes, but no grouping symbols, so your function would appear to be as follows:

. . . . .f(x) = 4/x² - sqrt[x³] + 1/sqrt[x] - 1

...which may also be formatted as:

. . . . .\(\displaystyle \L f(x)\, =\, \frac{4}{x^2}\, -\, \sqrt{x^3}\, +\, \frac{1}{\sqrt{x}}\, -\, 1\)

Is the above what you'd meant?

Thank you!

Eliz.

 

[yanarains]

YES EXACTLY WHAT I MEANT

That is exactly what I meant.

 

[stapel]

f(x)= 4/x^2-sqrt.x^3+1/ sqrt.x - 1

f(x)= 4(-2x) - 3x^-1/2 +1/2x^-3/2

Which f(x) are you supposed to be using? Or is the second function for a second exercise?

Also, please clarify what you mean when you say that some aspect of the function(s) "doesn't feel right". What, exactly, are you saying?

When you reply, please show how far you've gotten on finding f'(x). Thank you!

Eliz.

 

[yanarains]

The format that you had written is the only function. the latter information was my work. It don't feel like i am doing something right.

Let me try again hopefully in a more legible:
f(x) = 4/x^2 - sqrt[x^3] + 1/sqrt[x] - 1


=[4(x^2)^-1/2(2)] - (x^3)^-1/2 + (x^1/2
=8(x^2)^-1/2 +(3/2x)^-3/2 -1/2x^-3/2)

Is this right or is 4/x^2 turn into a -8?
thanks

 

[skeeter]

\(\displaystyle \L f(x) = \frac{4}{x^2} - \sqrt{x^3} + \frac{1}{\sqrt{x}} - 1\)

rewrite the function ...

\(\displaystyle \L f(x) = 4x^{-2} - x^{\frac{3}{2}} + x^{-\frac{1}{2}} - 1\)

use the power rule to find the derivative of each term ...

\(\displaystyle \L f'(x) = -8x^{-3} - \frac{3}{2}x^{\frac{1}{2}} - \frac{1}{2}x^{-\frac{3}{2}}\)

rewrite the derivative ...

\(\displaystyle \L f'(x) = -\frac{8}{x^3} - \frac{3\sqrt{x}}{2} - \frac{1}{2\sqrt{x^3}}\)

 

[stapel]

f(x) = 4/x^2 - sqrt[x^3] + 1/sqrt[x] - 1 =[4(x^2)^-1/2(2)] - (x^3)^-1/2 + (x^1/2

It looks as though you are saying that the derivative, f', is the same as the original function, f. But that isn't true, is it...? :shock:

Eliz.