Question

How do find the second derivative for `dy/dx = 5x^2 - 6/(y-2)`?

Answer 1

Refer to explanation

Explanation:

We know that `y'=dy/dx = 5x^2 - 6/(y-2)` hence

`(d^2y)/(d^2x)=d/dx(5x^2-6*(y-2)^(-1))=25x+6(y-2)^(-2)*(y)'`

But replacing the value of the first derivative we have that

`(d^2y)/(d^2x)=25x+6(y-2)^(-2)*(5x^2-6/(y-2))=25x+(30x^2)/((y-2)^2)-36/((y-2)^3)`