Question

If 5x^2 + y^4 = −9 then evaluate d^2y/dx^2 when x = 2 and y = 1.

Answer 1

implicit differentiation: \( \frac{d}{dx}(5x^2) + \frac{d}{dx}(y^4) = \frac{d}{dx}(-9)\)

you will get dy/dy at x = 2 and y = 1 from this.

and then do it again to get second deriv at x = 2 and y = 1.

Answer 2

So 10x+4y^3=-9?

Answer 3

5x^2 + y^4 = −9
10x+4y^3y'=0

Answer 4

10+12y^2y''=0

Answer 5

\(5x^2 + y^4 = −9\)
\(10x+4y^3y'=0\) gives you \(y'\)
\(10+12y^2y'.y'+4y^3y'' = 10+12y^2(y')^2+4y^3y''=0\) gives you \(y''\)