## mathcalculus 2 years ago Help: Find the slope of the tangent line to the curve (attached below)

1. mathcalculus

2. mathcalculus

I'm a little confused, where do i know to put d/dx and when to directly do the derivative..

3. pgpilot326

use implicit differentiation to find dy/dx and exaluate at the given point.

4. mathcalculus

i did, but thats where im confused... it's like i can take the derivative of -3x^2 but then should i put d/dx next to it... or just simply leave it -6x

5. mathcalculus

im getting mixed up.

6. mathcalculus

then also 3xy... derivative or not... i know i have to put d/dx

7. pgpilot326

if it's a function of x then take the derivative of the function and multiply by its differential, dx. Same with y. example. for x^2 you'd get 2x*dx, for y^2 you'd get 2y*dy

8. pgpilot326

for xy, use the product rule. y*dx + x*dy

9. mathcalculus

right, okay. let me try again

10. mathcalculus

so first it would be -6x*d/dx right?

11. pgpilot326

no... just -6x*dx

12. mathcalculus

and what about the 3 do i leave it out? and use product rule with xy?

13. mathcalculus

ok....

14. pgpilot326

3 is a constant so it oges along for the ride. also, d/dx is an operator. it says to take the derivative of whatever follows wrt x.

15. pgpilot326

goes

16. mathcalculus

with respect to x..

17. mathcalculus

i dont know ive been using d/dx whenever i see an x and dy/dx for a y

18. pgpilot326

dx is the differential of x... the change in x, if you will

19. pgpilot326

you could do dx/dx everytime you take a derivative of a function of x and dy/dx for a function of y... that's okay. but dx/dx is just 1.

20. mathcalculus

ok yes:) now we're on the same pg

21. mathcalculus

for the middle part, is it, 3x*dx/dx+y*dy/dy?

22. pgpilot326

3y*dx/dx+3x*dy/dx

23. pgpilot326

= 3y + 3x*dy/dx

24. mathcalculus

oh+|

25. pgpilot326

i 've got to go... so you can at least check... you should get 3 as the final answer. Good luck!

26. mathcalculus

thank you, i appreciate it.