Verified answer

Use implicit differentiation to find derivative given 3x²y-4y² = 2x? ......... (1)

Differentiate 3x²y using product formula. Thus –

d ( 3 x²y ) / dx

=> 3 d ( x²y ) / dx

=> 3 [ d(x²) / dx . y + x² dy/dx ]

=> 3 [ (2x) y + x² dy/dx ] .................... (2)

Also we know ----

d(4y²) / dx = (-8) y dy/dx ................... (3)

Now substitute these values in the given expression –

3 [ (2x) y + x² dy/dx ] + [(-8) y dy/dx ] = 2

=> 6 xy + 3 x² dy/dx - 8 y dy/dx = 2

=> 3 x² dy/dx - 8 y dy/dx = 2 - 6 xy

=> dy/dx = ( 2 - 6 xy ) / ( 3 x² - 8 y ) ................... Answer Answer

P.K.Tandon

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3x^2y' + 6xy - 8yy' = 2

(3x^2 -8y)y' = 2-6xy

y' = (2-6xy)/(3x^2 - 8y)