(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find derivative of y with respect to x.

Sin(xy) = Sinx Siny

2. Relevant equations

3. The attempt at a solution

Use chain rule (product rule for inner function) to differentiate the left. Use product rule to differentiate the right and I get the following:

cos(xy)(y+xy') = (cosx siny) + (cosy' sinx)

distribute the cos(xy) on the left to get:

ycos(xy) + xy'cos(xy) = (cosx siny) + (cosy' sinx)

Rearrange to get y' on one side, everything else on the other.

ycos(xy) - cosx siny = -xy'cos(xy) + cosy' sinx

Now what? I don't understand how I'd solve for y' from here. Inverse cosine?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Implicit differentiation

**Physics Forums | Science Articles, Homework Help, Discussion**