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Find dy/dx by implicit differentiation. 3x²+3 = ln 5xy²

This is what i did: 6x = D (ln 5x + ln y²) But i was thinking i could also use this way:

6x = D(5xy²)/5xy²

Are both ways the same?

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  • $\begingroup$ @AhalleySamuel: You should add parenthesis to avoid ambiguity ... $\endgroup$ – Adren Feb 25 '17 at 9:52
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Yes, you are right.

If you try the first one, we get, $$\frac{\mathrm{d}}{\mathrm{d}x} (\ln 5x + \ln y^2) = \frac{1}{5x}(\frac{\mathrm{d}}{\mathrm{d}x}(5x)) = \frac{1}{x}$$

In case of the second, we get, $$\frac{\frac{\mathrm{d}}{\mathrm{d}x}(5xy^2)}{5xy^2} = \frac{5y^2}{5xy^2} = \frac{1}{x}$$ yielding the same answer as before.

Hope it helps.

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  • $\begingroup$ Yea. Both ways arrive at the same results. Thanks man $\endgroup$ – Ashalley Samuel Mar 4 '17 at 3:04

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