Second implicit derivative Computation

Question

How would one compute the second implicit derivative of the equation x^e+y^pi=10?

Answer 1

x^e + y^π = 10

 

It looks like you should apply the power rule to differentiate the first term, and the power and chain rules to differentiate the second term.

 

ex^e-1 + πy^π-1y' = 0

 

Differentiate again.

 

(e - 1)ex^e-2 + (π - 1)πy^π-2y' + πy^π-1y'' = 0

 

You can then express y'' in terms of x and y'.