I'm supposed to find y'' in terms of x and y given x^5+y^5=2^5 I know how to do the first derivative, but I'm struggling with the second...

Question

I'm supposed to find y'' in terms of x and y given  x^5+y^5=2^5  I know how to do the first derivative, but I'm struggling with the second...

btaylor · Answer

what do you have for the first derivative?

anonymous · Answer

5x^4+5y^4*y'=0

anonymous · Answer

for the second my guess is 20x^3+20y^3*y'+5y^4*y''=0...

btaylor · Answer

That looks right, but you need to solve for y' and plug it into that equation. Then solve that giant mess for y''.

anonymous · Answer

so y' will be -x^4/y^4..

btaylor · Answer

yep.

anonymous · Answer

i get      (4x^4/y-4x^3)/y^4 ?

anonymous · Answer

that's y''= (4x^4/y-4x^3)/y^4

anonymous · Answer

I'm still doing something wrong...

btaylor · Answer

i think that's right...

anonymous · Answer

wait, when I take the derivative of  y'  it doesn't equal  y'',  it's more than that...do you know what it is @BTaylor?

zepdrix · Answer

No it's not more than that.$$\Large\bf\sf \frac{d}{dx}\frac{dy}{dx}\quad=\quad \frac{d^2y}{dx^2}\quad=\quad y''$$

isaiah.feynman · Answer

@josh55 are you clarified? |dw:1394350928979:dw|