How do you find #(df)/dy# and #(df)/dx# of #f(x,y)=(4x2y)/(4x+2y)#, using the quotient rule?
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To find ((df)/dy) and ((df)/dx) of (f(x,y)=(4x2y)/(4x+2y)) using the quotient rule:

Compute (df/dx): [df/dx = \frac{d}{dx} \left( \frac{4x  2y}{4x + 2y} \right) = \frac{(4)(4x + 2y)  (4x  2y)(4)}{(4x + 2y)^2}]

Compute (df/dy): [df/dy = \frac{d}{dy} \left( \frac{4x  2y}{4x + 2y} \right) = \frac{(2)(4x + 2y)  (4x  2y)(2)}{(4x + 2y)^2}]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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