Implicit differentiation

[halcyon reef]

May I know why 5y no need to put dy/dx?

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[severe sand]

I'm assuming the problem is to find dy/dx given that 5xy - y^3 = 8

[lunar lion]

toe

[severe sand]

now use the product rule to find d/dx (xy). You should get:

[lunar lion]

toe

[severe sand]

Substitute that into the equation at the bottom over here

And we get:

[lunar lion]

toe

[severe sand]

that's where the 5y at the front comes from

The coefficient in front of 5y is really just dx/dx, not dy/dx. Since dx/dx = 1, then we just have 5y × 1 or just 5y.

[halcyon reef]

Oh I see okok tq I get it 🙏

[vague bough]

uh, I don't think differentiation can be used like that

but eh

if it works, then good

[severe sand]

wdym

[tacit flower]

this is the only way not to treat differentiation as fraction