How do you differentiate y sin x = y

flatantsmu 2022-10-08 Answered
How do you differentiate y sin x = y
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Answers (1)

trutdelamodej0
Answered 2022-10-09 Author has 11 answers
You can use the product rule, like the usual. Just remember that the derivative of y with respect to x in d f d x is d y d x
With f ( x ) : y sin x = y
d f d x [ y sin x = y ] = y cos x + sin x ( d y d x ) = d y d x
d y d x [ 1 - sin x ] = y cos x
d y d x = y cos x 1 - sin x
If you check Wolfram Alpha, you'll see this, just multiplied by −1.
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Asked: use implicit differentiation to differentiate sin ( x y ).
My take on the matter:
Using the chain rule: d d x sin ( x y ) = cos ( x y ) d d x x y, then using the product rule on latter factor we get: d d x x y = y + x d y d x
Hence: d d x sin ( x y ) = y cos ( x y ) + x cos ( x y ) d y d x .
Is this correct?

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