Question

Help: Find the slope of the tangent line to the curve
(attached below)

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

im getting mixed up.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

right, okay. let me try again

Answer 9

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

Answer 10

no... just -6x*dx

Answer 11

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

Answer 12

ok....

Answer 13

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.

Answer 14

goes

Answer 15

with respect to x..

Answer 16

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

Answer 17

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

Answer 18

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.

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

= 3y + 3x*dy/dx

Answer 23

oh+|

Answer 24

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

Answer 25

thank you, i appreciate it.