# Differentiation by implicit

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?

• @AhalleySamuel: You should add parenthesis to avoid ambiguity ... – Adren Feb 25 '17 at 9:52

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.