Use implicitdifferentiationto findd^2 y/dx^2 if Also find Whatdoesthe
secondderivativerepresent?
Solution:
Solvingfordy/dx,
Differentiatingboth sidesimplicitlyagain(and usingthe quotientrule),
But sincedy/dx= 5x/4y, we substituteit into the secondderivative:
This is the secondderivativeofy.
The next step is to find :
Sincethe first derivativeof a functionrepresentsthe rate of changeof the functiony=f(x) with respectto
x, the secondderivativerepresentsthe rate of changeof the rate of changeof the function.For example,