Question

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Find the dy/dx:x^2y=siny​

Answer 1

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Step-by-step explanation:

What is the derivative, dy/dx, of the equation x^2y-e^2x=siny with an explanation?

Ben Newey, BSc Philosophy, Politics, and Economics, University of Warwick (2021)

Updated September 30 · Author has 2.3K answersand 2.2M answer views

Because this has both xxand yyterms it's best to use the ddxddx operator. Applying the operator to every term (and using the product rule when appropriate):

ddx(x2)y+ddx(y)x2–ddx(e2x)=ddx(siny)ddx(x2)y+ddx(y)x2–ddx(e2x)=ddx(sin⁡y)

ddx(y)=dydxddx(y)=dydx (this is what you've been doing when differentiating other things). You can differentiate sinysin⁡ywith respect to xxby using the chain rule: ddx(siny)=ddy(siny)dydxddx(sin⁡y)=ddy(sin⁡y)dydx (you can see how this works by pretending the operators are fractions).

Hence 2xy+x2dy/dx–2e2x