How do find the second derivative for $\frac{d y}{d x} = 5 x^{2} - \frac{6}{y - 2}$ $dy/dx = 5x^2 - 6/(y-2)$ ?

Question

3092 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-25T22:47:57

Refer to 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

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

How do find the second derivative for dy/dx = 5x^2 - 6/(y-2)dydx=5x2−6y−2dy/dx = 5x^2 - 6/(y-2)?