The procedure is to take the derivative with respect to
of both sides of the equation and then solve for
.
The right hand side of the equation above is zero because 32 is a constant.
To compute the left hand side, treat y as a function of x and use the chain rule every time you need to take its derivative:
- The derivative
follows from the power rule.
- To compute the second term, use the product rule:
.
- The third term is computed using the chain rule:
.
Combining the above yields
Solving for
gives the result