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How do you differentiate #e^sqrty-xy=6#?

Answer 1

William Abdalla

Use implicit differentiation ...

Using implicit differentiation, chain and product rules :

#(e^sqrty)xx(1/2)(y^(-1/2))xxy'-y-xy'=0#

Finally, solve for y'

#y'=y/[(e^sqrty)xx(1/2)(y^(-1/2))-x#

hope that helps

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Answer 2

Emily Ammerman

To differentiate ( e^{\sqrt{y}-xy}=6 ) with respect to ( x ), we can use the chain rule and the product rule. The derivative is:

[ \frac{d}{dx} \left( e^{\sqrt{y}-xy} \right) = e^{\sqrt{y}-xy} \left( -y - y'\sqrt{y} \right) ]

where ( y' ) is the derivative of ( y ) with respect to ( x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.