Math problem...see details...?

Question

Given y = 4x(cubed) + 2x(squared) and dx/dt = 1/2 at x=1. Find dy/dt.

Can anyone please figure this out and possibly explain this crap to me?

Answer 1

You use the Chain Rule, which probably has a Wikipedia page at
http://en.wikipedia.org/wiki/Chain_rule

If y is a function of x and x is a function of t, then

(dy/dt) = (dy/dx) (dx/dt)

Since y = 4x^3 + 2x^2 you have (dy/dx) = 12x^2 + 4x

So at x = 1 you have dy/dx = 16, dx/dt = 1/2, and therefore dy/dt = 8

Answer 2

this crap is called differentiation.. lol

anyhow, here's how it goes..

since y=4x(cubed)+2x(square) is given..
first, you find what dy/dx is..

dy/dx= (4)(3)x^(3-1) + (2)(2)x^(2-1) = 12x(square) + 4x

and since you know x=1, so u replace 1 into the x-values in dy/dx

therefore u should get, dy/dx=12+4 = 16

Now, that u know what dy/dx and dx/dt is, you can find dy/dt
because

dy/dt = (dx/dt)(dy/dx)

so dy/dt = (16)(0.5) = 8

hope u understood what i just explained, and good luck with any other differentiation or math problems that you have.. :)

Answer 3

Are you talking about dy/dt at x = 1 (y = 6) ?
If you want to get more general than that you'll need the expression for x(t).
As an example of why that is, consider that both
x(t) = 1/2 t
and x(t) = 1/4 t^2
both satisfy x'(1) = 1/2
but these will yield different values for dy/dt at other points.

if you are looking at the point x = 1, it looks like some of the other posts got it right.

Answer 4

its called differentiation.

use the power rule

dy/dt = 12x^2 (dx/dt) + 4x dx/dt
dy/dt= 12(1)^2(1/2) + 4(1) (1/2)
dy/dt= 8

Answer 5

The very first answer is correct. However, this stuff is not crap, this stuff is literally what makes the world go round as it does the rest of the planets and stars. I think Issac Newton would be keenly disappointed by your calling his methods of fluxions, crap.