Question

can someone please differentiate this simple equation?

Answer 1

\[x ^{2} = t\]

Answer 2

I am differentiating with respect to t.
d/dt(x^2)=d(t)/dt
d/dx(x^2)dx/dt=1
2x(dx)=dt

Answer 3

what is soo difficult in that?

Answer 4

i know the answer is 2xdx = dt. but i don't get how that is the answer :(. couldn't is have been x = sqrt(t) before starting to differentiate?

Answer 5

Yes tomiko :) Let's see how that would work out!\[\large x^2=t \qquad \rightarrow \qquad \color{royalblue}{x=\sqrt t}\]Probably should worry about a plus/minus when doing this, but whatev.
Taking the derivative with respect to t gives us,\[\large dx=\frac{1}{2\color{royalblue}{\sqrt t}}dt\]Do you see what's going to happen with the blue portion if we plugged it in?
You should get the same answer.

Answer 6

thank a lot @zepdrix