Final answer:
To find dy/dx when x = 4 and y = 16, differentiate the volume function V = (1/3)πx²y with respect to x, using the product rule and chain rule. Substituting the given values, solve for dy/dx.
Step-by-step explanation:
To find dy/dx when x = 4 and y = 16, we need to differentiate the volume function V = (1/3)πx²y with respect to x. Applying the product rule and chain rule, we have:
dV/dx = (1/3)π(2x)(y) + (1/3)πx²(dy/dx)
Substituting x = 4 and y = 16 into this equation, we can solve for dy/dx.
In calculus, differentiation is one of the two important concepts apart from integration. Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.
The most common example is the rate change of displacement with respect to time, called velocity. The opposite of finding a derivative is anti-differentiation.