## mathcalculus 2 years ago Derivative Question: Help (attached below)

1. mathcalculus

2. NoelGreco

3. satellite73

hint:$x^5\sqrt{x}=x^{5+\frac{1}{2}}=x^{\frac{11}{2}}$

4. mathcalculus

right.. 3x^(11/2)

5. NoelGreco

That's it, and go with a negative exponent on the second term to avoid the quotient rule.

6. mathcalculus

+ -4*x^-7/2 ?

7. NoelGreco

Yes.

8. mathcalculus

i got: 3x^(11/2)+14/x^9/2..

9. mathcalculus

@NoelGreco

10. NoelGreco

$3x ^{\frac{ 11 }{ 2 }}-4x ^{\frac{ -7 }{ 2 }}$ Now take the derivative.

11. mathcalculus

14x/x^9/2

12. mathcalculus

?

13. NoelGreco

The derivative of the second term is$\frac{ d }{ dx }3x ^{\frac{ 11 }{ 2 }}=\frac{ 33 }{ 2 }x ^{\frac{ 9 }{ 2 }}$ I don't know how you're trying to take the derivative, but you simply use the power rule on each term.

14. mathcalculus

huh?

15. mathcalculus

from 3x^ (11/2) + 14x^(-9/2)

16. mathcalculus

doesn't the x9/2 down

17. mathcalculus

@NoelGreco hey sorry to interrupt. but i just needed to figure this out before leaving..

18. satellite73

$\frac{d}{dx}14x^{-\frac{9}{2}}=-\frac{9}{2}\times 14x^{-\frac{9}{2}-1}$whatever that is

19. mathcalculus

this is my work so far:

20. sami-21

Before applying the power rule combine the terms as told you previously . $\Large f(x)=3x^5.x^\frac{1}{2}-\frac{-4}{x^3.x^\frac{1}{2}}$ combining the terms $\Large f(x)=3x^\frac{11}{2}-\frac{4}{x^\frac{7}{2}}$ $\Large f(x)=3x^\frac{11}{2}-4x^{-\frac{7}{2}}$ now Apply the Power rule.

21. mathcalculus

thank you are you still there @sami-21

22. mathcalculus

i have one question if you dont mind

23. mathcalculus

what if they ask: derivative of sqrt(6x)

24. mathcalculus

i dont know why i always messed them up

25. mathcalculus

i thought it would be like this: = 6x^(1/2) then =3x^(-1/2) =3/(x^(1/2)

26. mathcalculus

@sami-21

27. sami-21

yes that is correct.