Calculus/Calculus

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Expert: - 3/2/2011


Question
Let 4x^2+4x+xy=2 and y(2)=-11. Find y'(2) by implicit differentiation

Answer
It is given that y(2) = -11.  Checking this out gives 4(2^2) + 4(2) - 11(2) = 16 + 8 - 22 = 2,
and that is what is on the right side of the equation.

The 4x^2 is differentiated normally.

The 4x is differentiated normally.

The xy is differentiated as a product rule with the derivative of x being 1 and
the derivative of y being y'.

The derivative of the constant is 0.

Thus, to take the derivative gives 8x + 4 + xy' + y = 0.
From here, y' can be seen to be y' = -(8x+4+y)/x.

To find y', put in 2 for x and -11 for y, then this give y'.

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