Question

If y = 2x3 – 4x and dx, dt equals 4, find dy, dt when x = 1. Give only the numerical answer. For example, if dy, dt = 3, type only 3. I keep getting 2 buy it says that is wrong?

Answer 1

but*

Answer 2

Check your derivative:\[y=2x^3-4x~~\implies~~\frac{dy}{dt}=6x^2\color{red}{\frac{dx}{dt}}-4\]
You're differentiating with respect to a new variable \(t\), not \(x\), so you must differentiate implicitly on all variables.

Answer 3

Whoops, there's something missing above:
\[y=2x^3-4x~~\implies~~\frac{dy}{dt}=6x^2\color{red}{\frac{dx}{dt}}-4\color{blue}{\frac{dx}{dt}}\]

Answer 4

so would i fill in 4 for dx/dt and 1 for x?

Answer 5

Yes, you'll find that \(\dfrac{dy}{dt}\not=2\) :)

Answer 6

and that would give me 8

Answer 7

That's right

Answer 8

Thank YOU!!

Answer 9

yw

Answer 10

3x^3-2x dx/dt=3 and x =-2

Answer 11

Its doing the same thing as the last

Answer 12

so it would be -78? @SithsAndGiggles

Answer 13

No, not quite.
\[y=3x^3-2x~~\implies~~\frac{dy}{dt}=9x^2\frac{dx}{dt}-2\frac{dx}{dt}=9(-2)^2(3)-2(3)\]