1. ## Implicit differentiation

Hello people,

This question just doesnt help me at all!

4x^4 + 8xy - 16y = 14

using implicit differentiation,

Help me out please with steps and explain.

Thank you so much!!!!!!

2. If a function is defined in implicit form...

$\displaystyle f(x,y)=0$ (1)

... then is...

$\displaystyle y^{'} = -\frac{f_{x}^{'} (x,y)}{f_{y}^{'} (x,y)}$ (2)

$\displaystyle f(x,y)= 4x^{4} + 8xy -16y -14$

$\displaystyle f_{x}^{'} (x,y) = 16x^{3} + 8y$

$\displaystyle f_{y}^{'} (x,y) = 8x - 16$ (3)

... so that...

$\displaystyle y^{'} = - \frac{2x^{3} + y}{x-2}$ (4)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. Originally Posted by chisigma
If a function is defined in implicit form...

$\displaystyle f(x,y)=0$ (1)

... then is...

$\displaystyle y^{'} = -\frac{f_{x}^{'} (x,y)}{f_{y}^{'} (x,y)}$ (2)

$\displaystyle f(x,y)= 4x^{4} + 8xy -16y -14$

$\displaystyle f_{x}^{'} (x,y) = 16x^{3} + 8y$

$\displaystyle f_{y}^{'} (x,y) = 8x - 16$ (3)

... so that...

$\displaystyle y^{'} = - \frac{2x^{3} + y}{x-2}$ (4)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
I completely understand that until you get to step (4)

Wait I get it, your reducing with 8. I thought you weren't allowed to do that though.