implicit differentiation

[renegade05]

I need some help differentiating the following implicitly defined curve:

$\displaystyle 2^{(\frac{x}{y})}+2x^2y^3=26$

My guess is:

$\displaystyle 2^{(\frac{x}{y})}\ln{2}(y-\frac{x}{y^2}\frac{dy}{dx})+(4xy^3+6x^2y^2\frac{dy}{dx})=0$

I am pretty sure the the second half (after the first +) of the equation is right, the $\displaystyle 2^{(\frac{x}{y})}$ is what i am unsure about.

Please help, Thanks!

obvs simplifying is not necessary.

 

[soroban]

Hello, renegade05!

Your "Quotient Formula" is off.

$\displaystyle \text{The deriative of: }2^{\frac{x}{y}}\,\text{ is: }\; 2^{\frac{x}{y}}\cdot \ln2 \cdot\left(\frac{y - x\frac{dy}{dx}}{y^2}\right)$

 

[renegade05]

oh ya.. i dont know how i did that. sweet thanks!