How do you implicitly differentiate # 2y^2 - 3x^2y + x siny= 1/(x-y)#?
We start with:
We use the chain rule to implicitly differentiate:
Combine terms with y':
Get rid of fraction on RHS:
Move all y' terms to RHS:
Factor out y':
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To implicitly differentiate the given expression, follow these steps:
- Differentiate each term of the expression with respect to .
- Treat as a function of and use the chain rule when differentiating terms involving .
- Solve for after differentiating.
Differentiating each term:
Using the chain rule:
Putting it all together:
Now, solve for .
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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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