Answer to Question #262723 in Calculus for Alunsina

Question

If x⁴+y⁴=16, use the following steps yo find y''.

a. Use implicit differentiation to find y'.

b. Use the Quotient Rule to differentiate the expression for y' from part (a). Express your answer in terms of x and y only.

Answer 1

a.

$4x^3+4y^3y'=0$

$y'=-x^3/y^3$

b.

$y''=-\frac{3x^2y^3-3y^2x^3y'}{y^6}=-\frac{3x^2y^3+3x^6/y}{y^6}=-\frac{3x^2y^4+3x^6}{y^7}$