Final answer:
To find the differential dy=__dx for the equation y=3sqrt(x), we can differentiate both sides of the equation with respect to x using the power rule.
Step-by-step explanation:
To find the differential dy=__dx for the equation y=3sqrt(x), we can start by expressing y in terms of x and then differentiate both sides of the equation with respect to x.
Given that y=3sqrt(x), we can rewrite it as y=3x^(1/2).
Next, we differentiate both sides using the power rule for differentiation, which states that d/dx(x^n) = nx^(n-1).
For the given equation, differentiating y=3x^(1/2) gives us dy/dx = (3/2)x^(-1/2).