How do you find #dy/dx# by implicit differentiation given #y=sqrt(xy+1)#?
Square both sides to eliminate the need to use the chain rule.
Now use implicit differentiation and the product rule to find the derivative.
Hopefully this helps!
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To find ( \frac{dy}{dx} ) by implicit differentiation for the equation ( y = \sqrt{xy + 1} ), follow these steps:
- Differentiate both sides of the equation with respect to ( x ).
- Apply the chain rule when differentiating ( \sqrt{xy + 1} ).
- Solve for ( \frac{dy}{dx} ) after differentiating each term.
The result will be:
[ \frac{dy}{dx} = \frac{1}{2\sqrt{xy + 1}}(y + x\frac{dy}{dx}) ]
Then, solve for ( \frac{dy}{dx} ).
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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.
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.
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.
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.

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