Find
dy/dt
when
y = 2x2 + 2x + 4
and
dx/dt = 14
when
x = 7.
FORMAT WRONG ABOVE....
Correct one is..
Find
dy/dt
when
y = 2x^2 + 2x + 4
and
dx/dt = 14
when
x = 7.
just use the chain rule. Since x and y are both functions of t,
dy/dt = (4x+2) dx/dt
Now just plug in your numbers
To find dy/dt, we need to differentiate the given function y = 2x^2 + 2x + 4 with respect to t, assuming x is a dependent variable.
Step 1: Differentiate the function with respect to x. This means finding dy/dx.
dy/dx = d/dx(2x^2 + 2x + 4)
= d(2x^2)/dx + d(2x)/dx + d(4)/dx
= 4x + 2
Step 2: Apply the chain rule to find dy/dt.
dy/dt = dy/dx * dx/dt
Given dx/dt = 14, we substitute this into the equation:
dy/dt = (4x + 2) * dx/dt
= (4x + 2) * 14
Now that we have the value of x, which is given as x = 7, we can substitute it into the equation:
dy/dt = (4 * 7 + 2) * 14
= (28 + 2) * 14
= 30 * 14
= 420
Therefore, dy/dt = 420 when y = 2x^2 + 2x + 4 and dx/dt = 14, given x = 7.