# How do you find #dy/dx# by implicit differentiation given #x^4+y^4=5#?

The answer is

Let's do the differentiation

Therefore,

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To find ( \frac{dy}{dx} ) by implicit differentiation for the equation ( x^4 + y^4 = 5 ), follow these steps:

- Differentiate both sides of the equation with respect to ( x ).
- Treat ( y ) as a function of ( x ) and use the chain rule when differentiating terms containing ( y ).
- Solve the resulting equation for ( \frac{dy}{dx} ).

Differentiating both sides with respect to ( x ) yields:

[ 4x^3 + 4y^3 \frac{dy}{dx} = 0 ]

Rearranging terms to solve for ( \frac{dy}{dx} ):

[ \frac{dy}{dx} = -\frac{x^3}{y^3} ]

This is the derivative ( \frac{dy}{dx} ) for the given implicit equation.

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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.

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