# Implicit differentiation in multiple variables

1. Mar 20, 2013

### groovy958

So, as the title may have given away, I'm trying to figure out implicit differentiation in the multiple variable context. I thought a good practice would be the law of cosines, aka
c^2 = a^2 + b^2 - 2abcosθ.
So I'm trying to find ∂θ/∂a, ∂θ/db, ∂θ/dc.
I tried solving for θ and then taking partials, but that seems like the wrong way to do it. Any suggestions?

2. Mar 20, 2013

### fzero

Solve for $\cos\theta$ and use the chain rule to express, say, $\partial \theta/\partial a$ in terms of $\partial (\cos \theta)/\partial a$. You can use a trig identity to rewrite the sin function in terms of the original cos.