Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
(a) Find `dy/dt` ,given `x=2` and `dx/dt =11`
(b) Find `dx/dt` , given `x=1` and `dy/dt=-7`
If someone can explain the steps so I understand these types of problems it would mean a lot.
The given equation is:
Take the derivative with respect to t on both sides of the equation.
Note that the derivative of constant is zero. So right side becomes:
For the right side, apply the power rule which is`(u*v)'=v*u' + u*v'`.
Now that derivative of the equation with respect to x is known, use this and the given equation to solve the two problems.
(A) `x=2` and `dx/dt=11` , `dy/dt=?`
Before substituting the given values to the derivative, solve for y first.
To do so, plug-in x=2 to:
Now that value of y is known, plug-in x=2, y=1 and `dx/dt=11` to:
Hence, when `x=2` and `dx/dt=11` , `dy/dt=-11/2` .
(B) `x=1` and `dy/dt=-7` , `dx/dt= ?`
Do the same steps as above. Plug-in x=1 to the given equation to solve for y.
Then, substitute x=1, y=2 and `dy/dt=-7` to:
Hence, when `x=1` and `dy/dt=-7` , `dx/dt=7/2` .