# Thread: Implicit Differentiation Check

1. ## Implicit Differentiation Check

find dy/dx using implicit differentiation

cos(x)+tan(xy)+8=7

First i change to cos(x)+tan(xy)+1=0

Im using -Fx(x,y) / Fy(x,y)

Fx= -sin(x)+ysec2(xy)

Fy= xsec2(xy)

dy/dx= sin(x)+ysec2(xy) / xsec2(xy)

Right or wrong? Thanks.

2. ## Re: Implicit Differentiation Check

If$\displaystyle F_x= -sin(x)+ysec^2(xy)$ wouldn't $\displaystyle -F_x= sin(x)-ysec^2(xy)$ ?

3. ## Re: Implicit Differentiation Check

Yes. I believe so. Thats what i did on my last step. But i dont know where to go from there to get the final answer.

4. ## Re: Implicit Differentiation Check

Originally Posted by tastylick
Yes. I believe so. Thats what i did on my last step. But i dont know where to go from there to get the final answer.
I think what MadSoulz was getting at is that you wrote $\displaystyle \dfrac{dy}{dx} = \dfrac{\sin(x) + y\sec^2(xy)}{x\sec^2(xy)}$. The numerator is not $\displaystyle -F_x$ which would have a negative sign between $\displaystyle \sin(x)$ and $\displaystyle y\sec^2(xy)$.

5. ## Re: Implicit Differentiation Check

So it should be

dy/dx= sin(x)-ysec2(xy) / xsec2(xy) correct.

But where to take it from there?

6. ## Re: Implicit Differentiation Check

Originally Posted by tastylick
But where to take it from there?
I believe you're done.

7. ## Re: Implicit Differentiation Check

Ah ok. I emailed my professor about this question and it turns out it was a mistake on her part. Yes my answer is correct. Thank you all for the help.