# Implicit differentiation

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implicit differentiation of x^3y^2-5x^2y+x=1

• Implicit differentiation -

what is...

3x^2y^2 dx+2x^3ydy-10xydx-5x^2dy+dx=0

gather terms...

dx(3x^2y^2-10xy+1)+dy(2x^3y-5x^2)=0

check this, easy to make a typo

• Implicit differentiation -

3x^2 y^2 + 2x^3 y y' - 10xy - 5x^2 y' + 1 = 0
y'(2x^3y - 5x^2) = -(3x^2y^2 - 10xy + 1)

y' = (10xy - 3x^2y^2 - 1)/(2x^3y - 5x^2)

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