Implicit Functions

Implicit diff is an application of chain rule.

we understand in this situation (Q14) that we might rearrange eqn to give y = f(x), but we needn't bother when differentiating m but we must treat y as a function of x.
Our target is to carry out the operation d/dx on each term of the eqn, but we cannot carry out that operation per se on a y-term.
instead, we carry out d/dy on a y-term, then times by dy/dx so that effectively the 'dy' terms cancel.

so for example, d/dx(cosy)
becomes
(dy/dx).d/dy(cosy)

= (-siny)(dy/dx)

Can you finish off this question, now?

Not necessarily.

You might try sqrt(2)sin(y+pi/4) as the Rsin(theta + alpha) form of the original.

Then dx/dy

then reciprocal

then find sqrt(2)cos(y+pi/4) in terms of x


Doing this, I've found dy/dx in terms of x only, then second diff is straight forward.

How to find sqrt(2)cos(y+pi/4) in terms of x ? I'm not very good at this and not getting near the answer. Would prefer to see the solution, understand it quickly and move on eventhough this is not the common protocol on this forum.