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

1. IrishBoy123

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.

2. anonymous

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

3. anonymous

5x^2 + y^4 = −9 10x+4y^3y'=0

4. anonymous

10+12y^2y''=0

5. IrishBoy123

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