Very hard Math problem derivative please help: f(x)=26-2x3 / 9-x2 its a division

[lengo]

Hi i need help to find a functions derivative

f(x)=26-2x³ / 9-x² its a division

also i need to find its second derivative

 

[lengo]

Problem with derivatives please help

I have to find a functions derivative

f(x)= 26-2x³ / 9-x<sup>2

ive tried solvin it but i keep getting stuck please help!

also i have to find its second derivative</sup>

 

[stapel]

Hi i need help to find a functions derivative

f(x)=26-2x³ / 9-x² its a division

Okay, but which part is divided by what? Is any of the following correct?

. . . . .\(\displaystyle \mbox{a. }\, f(x)\, =\, 26\, -\, \dfrac{2x^3}{9}\, -\, x^2\)

. . . . .\(\displaystyle \mbox{b. }\, f(x)\, =\, \dfrac{26\, -\, 2x^3}{9}\, -\, x^2\)

. . . . .\(\displaystyle \mbox{c. }\, f(x)\, =\, 26\, -\, \dfrac{2x^3}{9\, -\, x^2}\)

. . . . .\(\displaystyle \mbox{d. }\, f(x)\, =\, \dfrac{26\, -\, 2x^3}{9\, -\, x^2}\)

(Option (a) is what you've posted. I suspect that you mean Option (b), Option (c), or Option (d), however.)

When you reply, please show all of your steps in applying the Quotient Rule to this function.

also i need to find its second derivative

Where are you stuck in applying the Quotient Rule to the first derivative?

Please be complete. Thank you!

 

[UCdavisEcon]

I assume he means option d.

In such case, call the numerator (26-2x^2), f(x). Call the denominator (9-x^2), g(x)

Apply, the quotient rule for differentiation, (f'(x)*g(x) - g'(x)*f(x) ) / (g(x))^2