Find the total derivative dz/dt, given
z=f(x,y,t) where x=a+bt and y=c+dt
Without specifying the f(x,y,t) function, you can only give a general formula.
dz/dt(total) = �Ýz/�Ýx*dx/dt + �Ýz/�Ýy*dy/ dt + �Ýz/�Ýt
where all of the z derivatives on the right are partial derivatives.
dz/dt(total) = b �Ýz/�Ýx+ c �Ýz/�Ýy + �Ýz/�Ýt
I won't know if the �Ý symbol will display properly until I send this.
the "del" (slanted Greek d) symbol should have appeared where you see
�Ýz/
Idon't know this answer
To find the total derivative dz/dt, we need to find the partial derivatives of z with respect to x, y, and t, and then multiply them by the corresponding rates of change.
Given that z is a function of x, y, and t where:
x = a + bt
y = c + dt
We need to apply the chain rule to find the derivative dz/dt.
The chain rule states that if z is a function of x, y, and t, and x and y are functions of t, then the total derivative dz/dt is given by:
dz/dt = ∂z/∂x * dx/dt + ∂z/∂y * dy/dt + ∂z/∂t
First, let's find the partial derivatives of z with respect to x, y, and t.
∂z/∂x represents the partial derivative of z with respect to x.
∂z/∂y represents the partial derivative of z with respect to y.
∂z/∂t represents the partial derivative of z with respect to t.
Once we have these partial derivatives, we can substitute the values of x, y, and t into them and calculate the total derivative dz/dt.
Note: The values of a, b, c, d, and t are not provided, so you would need to substitute those with appropriate numerical values in order to obtain a specific answer.