I suppose this is implicit differentiation... The problem:
find yprime given
so I then simplified it to
Is this okay? Are there any errors, or can I move forward and work the algebra?
I suppose this is implicit differentiation... The problem:
find yprime given
so I then simplified it to
Is this okay? Are there any errors, or can I move forward and work the algebra?
Just in case a picture helps (and if not just ignore!) ...
... where
... is the chain rule, and...
... the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
On the right you have the chain rule wrapped inside the product rule - which you say you have ok. Actually I wouldn't have bothered posting except you missed out the chain in the second term - and I see now you didn't miss it at all first time round...
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I wish I could write fluently in this math language, but if you look at what I have so far, do I isolate the dy/dx's on the right side and bring everything else over to the other side? I'm pretty sure I keep gett dy/dx - dy/dx on the right when I simplify and move the non dy/dx's to the other side.
so I'm seeing another one of my errors where I thought I had to differentiate the y inside the cos and the sin on the RHS. That's why I was getting dy/dx on both sides and when I would try to isolate them to a side, they would cancel each other.
Would I then simplify it so that the only thing on that one side of the equation is dy/dx then?