When you differentiate y, stick a dy/dx beside it and then solve for dy/dx.
Solve for dy/dx.
I would like to point out that means the derivative of y with respect to x. In actuality, you solve both x and y in the exact same manner, it just doesn't look this way because which is usually an invisible coefficient.
For example, the derivative of is
and , so
Another way of saying would be y prime, or .
So for your problem:
Prep - First, you need to know the Power Rule and the Chain Rule, the Power Rule says that the derivative of with respect to x is equal to . So for example, This can be proven, but that's beyond the scope of this post. Don't get confused by It just means the derivative of ... with respect to x, where ... is whatever it is being multiplied by, in this case .
The Chain Rule says that the derivative of is equal to . Remember that . So if , and , then . Now differentiate, So, just fill in the equation, , because the derivative of is 1.
Step1 - differentiate both sides:
This entire step is Power Rule combined with Chain Rule, can be looked at as 2 functions, and . So . This means and or
Step2 - Simplify dx/dx as 1
step3 - Combine like terms (put any on the same side, and anything else on the other side)
step4 - Factor out
step5 - Solve for in this case, it means divide out everything it is being multiplied by.
So anyway, unless I messed up somewhere, that's the correct process for finding the answer for this type of a question.