Equation; $\displaystyle y = 2(x^2 - 3x)$
Find;
a) dy/dt
b) dx/dt
Given;
a) x = 3, dx/dt = 2
b) x = 1, dy/dt = 5
How do I go about solving this? I'm confused as to the procedure I need to use. A step-by-step solution would be greatly appreciated.
Equation; $\displaystyle y = 2(x^2 - 3x)$
Find;
a) dy/dt
b) dx/dt
Given;
a) x = 3, dx/dt = 2
b) x = 1, dy/dt = 5
How do I go about solving this? I'm confused as to the procedure I need to use. A step-by-step solution would be greatly appreciated.
$\displaystyle y = 2(x^2 - 3x)$
and we are assuming that the functions x = x(t) and y = y(t). So we do this implicitly:
$\displaystyle \frac{dy}{dt} = 4x \frac{dx}{dt} - 6 \frac{dx}{dt}$
Thus for part a you have x = 3 and dx/dt = 2 so
$\displaystyle \frac{dy}{dt} = 4(3)(2) - 6(2) = 12$
You try the second one.
-Dan
I'm having trouble with something. The topic question was fine because it only had 3 variables, 2 of which were given, so you just had to isolate the 3rd one and solve for it. But for this one, there's 4 variables; $\displaystyle xy' + x'y = 0$. You're asked to find the value for y' while given x and x'. How could I solve that? I have 2 unknown variables. (y' and y)
BTW; x = 8, x' = 10.