## amy0799 one year ago find derivative of the algebraic function

1. amy0799

$f(x)=x ^{5}(1-\frac{ 6 }{ x+5 })$

2. welshfella

first expand the bracket - find derivative of x^5 then use the quotient rule to differentiate the fraction

3. amy0799

c$\frac{ x ^{5} (x-1)}{ x+5 }$ can I do this?

4. welshfella

or if you prefer you can use the product / chain rules

5. welshfella

how did you get that?

i think he took the lcm

7. amy0799

$1-\left( \frac{ 6 }{ x+5 } \right) = \frac{ x-1 }{ x+5 }$

correct

9. amy0799

so then $\frac{ x ^{6}-x ^{5} }{ x+5 }$ I would just use the quotient rule?

10. welshfella

yes

11. amy0799

the answer would be $f'(x)=\frac{ 5x ^{6}+26x ^{5}-25x ^{4} }{ (x+5)^{2}}$?

correct

:)

14. welshfella

yes i get that too

15. amy0799

cool thanks!

16. welshfella

I'm slowing up in my old age lol!

@amy0799 thats really nice

18. welshfella

yes

19. welshfella

looking at it again I would have used the product rule because the algebra is easier...

@welshfella its okay:)

21. welshfella

lol - it has to be..