1. differentiation check!!

hey can someone check if this is correct. Just a differentiation of a function.

$\displaystyle f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})$

differentiated to:

$\displaystyle f '(x) = 20x^4 - 13 - 24x^{-4} - (\frac{4}{x^2}) - (\frac{15}{x^4})$

correct?

2. Originally Posted by jvignacio
hey can someone check if this is correct. Just a differentiation of a function.

$\displaystyle f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})$

differentiated to:

$\displaystyle f '(x) = 20x^4 - 13 - 24x^{-4} - (\frac{4}{x^2}) - (\frac{15}{x^4})$

correct?
Mostly correct except for the derivative of $\displaystyle 8\sqrt[3]{x}$.

Remember, this is $\displaystyle 8x^{\frac13}$.

Also, there is a sign error when you differentiated $\displaystyle - \left(\frac{5}{x^3}\right)$.

3. Not quite. There's a wrong sign at the end, and the differential of the cubic root is not right either. Perhaps you should write it $\displaystyle \sqrt[3]{x}=x^{\frac{1}{3}}$ to ease the differentiation.

4. $\displaystyle f '(x) = 20x^4 - 13 - \frac{8}{3}x^{\frac{-2}{3}} - (\frac{4}{x^2}) + (\frac{15}{x^4})$

better?

5. Still a problem with the root: the derivative of $\displaystyle \sqrt[3]{x}$ is $\displaystyle +\frac{1}{3}x^{-2/3}$, hence...

O wait, it just changed. There's still a problem: there is a + in front of the root.

6. Originally Posted by Laurent
Still a problem with the root: the derivative of $\displaystyle \sqrt[3]{x}$ is $\displaystyle +\frac{1}{3}x^{-2/3}$, hence...

O wait, it just changed. There's still a problem: there is a + in front of the root.
yes i noticed that aswell!!! silly me. thank u for the help

7. Originally Posted by jvignacio
hey can someone check if this is correct. Just a differentiation of a function.

$\displaystyle f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})$

differentiated to:

$\displaystyle f '(x) = 20x^4 - 13 - 24x^{-4} - (\frac{4}{x^2}) - (\frac{15}{x^4})$

correct?
See here,
$\displaystyle f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})$

$\displaystyle f (x) = 4x^5 - 13x + 8 x^{\frac{1}{3}} - 9 + 4{x}^{-1} - 5x^{-3}$

Differentiated to:

$\displaystyle f '(x) = 20x^4 - 13 + \frac{8}{3}x^{\frac{-2}{3}} - (\frac{4}{x^2}) + (\frac{15}{x^4})$

$\displaystyle f '(x) = 20x^4 - 13 + \frac{8}{\sqrt[3]{x^2}} - (\frac{4}{x^2}) + (\frac{15}{x^4})$