Differentiate both sides with respect to x

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SUMMARY

The differentiation of the equation x^5 log_{2}y - 10 = 0 with respect to x yields dy/dx = -50y ln2 / x^6. The differentiation process correctly applies the product rule for the first term and the chain rule for the logarithmic term. The result accurately expresses the derivative in terms of both x and y, confirming the correctness of the calculations presented in the discussion.

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Clari
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Find dy/dx.

[tex]x^5 log_{2}y-10 = 0[/tex]
Differentiate both sides with respect to x.
[tex]5x^4 log_{2}y + x^5/ (y ln2) dy/dx = 0[/tex]
[tex]dy/dx = -50y ln2 / x^6[/tex]

Is it correct? please tell me..
 
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Yes, it is correct.
 


Yes, your differentiation is correct. The product rule was used to differentiate the first term, and the chain rule was used to differentiate the logarithmic term. The result is a derivative in terms of both x and y, which can be simplified further if needed. Great job!
 

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