## LilySwan Group Title find dy/dx if (ax+cx^5)/kx^8 2 months ago 2 months ago

1. myininaya Group Title

a,c, and k are constants?

2. LilySwan Group Title

yes

3. micahwood50 Group Title

Just use quotient rule.

4. LilySwan Group Title

got stucked at one point

5. micahwood50 Group Title

$$\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}$$

6. LilySwan Group Title

why can we solve the numerator part first

7. micahwood50 Group Title

treat constant as if they are just "number", and not variable.

8. myininaya Group Title

@LilySwan Did you have a problem with finding derivative of the top or the bottom? That is what you need to plug into @micahwood50 's formula. what do you mean solve the numerator? You shouldn't be solving. You should be differentiating it. What is the derivative of the top part of your fraction?

9. LilySwan Group Title

for the upper part 5cx^4 +a

10. micahwood50 Group Title

Right f'(x) = a+5cx^4

11. micahwood50 Group Title

Can you find g'(x)?

12. LilySwan Group Title

for the lower part it will be 8kx^7

13. micahwood50 Group Title

Yep. So you have f(x) = ax+cx^5, f'(x) = a+5cx^4, g(x) = kx^8, g'(x) = 8kx^7 Just plug these in formula given above then simplify.

14. micahwood50 Group Title

Can you do it? @LilySwan

15. LilySwan Group Title

trying wait

16. LilySwan Group Title

i was told to use this formula $\frac{ d }{ dx }(\frac{ u}{ v }) =\frac{ (v \frac{ du }{ dx })-(u \frac{ dv }{ dx }) }{ v^2 }$

17. myininaya Group Title

same formula different notation

18. LilySwan Group Title

?

19. myininaya Group Title

$\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}$ if you want you can replace the f's with u's the g's with v's the ' things with d/dx and you have the same formula

20. LilySwan Group Title

$5cx^4+a.kx^8 - ax+cx^5. 8kx^7/(kx^8)^2$

21. myininaya Group Title

$\frac{(5cx^4+a)(kx^8)-(ax+cx^5)(8kx^7)}{(kx^8)^2}$ i think this is what you mean

22. LilySwan Group Title

yes

23. LilySwan Group Title

what should i be doing the next

24. myininaya Group Title

guess you could multiply things out on top and also use law of exponents on the bottom to simplify the bottom