What is the derivative of #x^2+y^2=5xy#?

Answer 1

I found: #(dy)/(dx)=(5y-2x)/(2y-5x)#

You can use implicit derivation considering that #y# represents a fuction of #x# such as #y=f(x)# and has to be derived accordingly. You get: #2x+2y(dy)/(dx)=5y+5x(dy)/(dx)# collecting #(dy)/(dx)#: #(dy)/(dx)[2y-5x]=5y-2x# and: #(dy)/(dx)=(5y-2x)/(2y-5x)#

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Answer 2

Aurora Alvarado

To find the derivative of (x^2 + y^2 = 5xy) implicitly, differentiate both sides of the equation with respect to (x):

[2x + 2y \frac{dy}{dx} = 5y + 5x \frac{dy}{dx}]

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

[2y \frac{dy}{dx} - 5x \frac{dy}{dx} = 5y - 2x]

[\frac{dy}{dx}(2y - 5x) = 5y - 2x]

[\frac{dy}{dx} = \frac{5y - 2x}{2y - 5x}]

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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.