Find dy/dx by implicit differentiation. $$ \left(2 x^{2}+3 y^{2}\right)^{5 / 2}=x $$
Added by Tanya G.
Step 1
Let's define u as the expression inside the parentheses: $$ u=2x^2+3y^2 $$ Then, we have: $$ \frac{d}{dx}\left(u^{5/2}\right)=\frac{d}{du}\left(u^{5/2}\right)\cdot\frac{du}{dx}= \frac{5}{2}u^{3/2}\cdot\frac{d}{dx}(2x^2+3y^2) $$ Using the chain rule again, we Show more…
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