Question

If y = -8 x^3 - 6 x, determine dy/dt when x = -4 and dx/dt = 3 .

Answer 1

I responded on your last question...
but I will try again

Answer 2

we know x and y are functions of t because it tells us to find dy/dt given dx/dt=3

Answer 3

anyways that means we need chain rule for each term

Answer 4

\[\frac{d(y)}{dt}=\frac{dy}{dt} \\ \frac{d(-8x^3)}{dt}=?\]

Answer 5

use power rule along with chain rule

Answer 6

I dont think you need the chain rule... Isnt it just basic power rule?

Answer 7

\[y'=-24x^2-6\]

Answer 8

where are you going to put that dx/dt is 3 if you don't use chain rule @OdinMW ?

Answer 9

@ericksol96 can you differentiate (-8x^3) w.r.t t?

Answer 10

@freckles It'll be -24x^2 right?

Answer 11

well times the derivative of x w.r.t t

Answer 12

\[\frac{d(x^n)}{dt}=nx^{n-1}\frac{dx}{dt}\]

Answer 13

\[\frac{dy}{dx}=-24x^2 \frac{dx}{dt}-6 \frac{dx}{dt}\]
replace dx/dt with 3
and x with -4

Answer 14

@freckles so its -24(-4)^2(3) - 6(3)

Answer 15

also that dy/dt for that one part

Answer 16

and yes

Answer 17

\[\frac{dy}{dt}=-24x^2 \frac{dx}{dt}-6 \frac{dx}{dt} \\ =-24(-4)^2(3)-6(3)\]

Answer 18

Alternatively, you can do it this way:

\[y(x)=-8x^3-6x\]\[\frac{dy}{dt}=-24x^2-6\]\[\frac{dy}{dt} (-4)=-24(-4)^2-6=-24*16-6=-390\]\[\frac{dy}{dt}=\frac{dy}{dx} * \frac{dx}{dt} = -390*3=-1170 \]

Answer 19

yeah that works to

Answer 20

@freckles @tom982 thanks guys, I understand it better :)

Answer 21

No problem, glad you understand it.