Pregunta: Let (x + 16)(y + 25) = x4 − y8 . Compute dydx.

Given that, $(\mathrm{x}+16)(\mathrm{y}+25)={\mathrm{x}}^4-{\mathrm{y}}^8\dots \dots \dots \dots .\left(\mathrm{i}\right)$

Differentiating $\left(\mathrm{i}\right)$ with respect to $\mathrm{x},$ we have

$(\mathrm{x}+16)\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}(\mathrm{y}+25)+(\mathrm{y}+25)\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}(\mathrm{x}+16)=\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left({\mathrm{x}}^4\right)-\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left({\mathrm{y}}^8\right)$