Question

Find y'' in terms of x and y by implicit differentiation.
x^4+y^4=3^4

working on this for a while please help

Answer 1

take the derivative as you would

Answer 2

\[4x^3+4y^3(\frac{ dy }{ dx })=0\]\[\frac{ dy }{ dx }=- \frac{ x^3 }{ y^3 }\]\[12x^2+12y^2(\frac{ dy }{ dx })+\frac{ d^2y }{ dx^2 }(4y^2)=0\]\[\frac{ d^2y }{ dx^2 }=\frac{ x^3 }{ 48y^3 }-\frac{ 3x^2 }{ y^2}=\frac{ x^3-144x^2y }{ 48y^3 }\]

Answer 3

Sorry, I made a mistake in the above math in the second step. This is the second derivative now that I have fixed my mistake:

\[\frac{ d^2y }{ dx^2 }=\frac{ x^6-144x^2y^4 }{ 48y^7 }\]
@abb0t

Answer 4

@Solongos