Find the derivatives given Z = 3y² where y = 2x + 5
To find the derivative of Z with respect to x, we first need to find the derivative of y with respect to x using the chain rule.
y = 2x + 5
dy/dx = 2
Now we can find the derivative of Z with respect to x using the chain rule:
dZ/dx = d/dx (3y²)
dZ/dx = 6y(dy/dx)
dZ/dx = 6(2x + 5)(2)
dZ/dx = 12(2x + 5)
dZ/dx = 24x + 60
Therefore, the derivative of Z = 3y² with respect to x is 24x + 60.