# Thread: help with implicit differentiation

1. ## help with implicit differentiation

sin(xy)=e^xy

should i use product or chain rule on the left side of the equation? I just started doing these and I am a bit confused. Thanks for any help

2. Like an onion, you must peel back the layers, working from the outside in. That means chain rule first, with a product rule inside. On the RHS, is it (e^x)y or e^(xy)? You want to be explicit with parentheses.

3. Originally Posted by Ackbeet
Like an onion, you must peel back the layers, working from the outside in. That means chain rule first, with a product rule inside. On the RHS, is it (e^x)y or e^(xy)? You want to be explicit with parentheses.
For the left hand side may I ask Ackbeet: are you assuming that y is a function of x in order to use both the chain rule and product rule when differentiating wrt x?

I would have just use the chain rule and treat y as constant...? I mean having z=f(xy) doesnt mean that y is a function of x right?

4. The title is the clue bugatti.

Assuming you mean e^(xy), then you want d/dx(xy)*e^(xy).

5. Originally Posted by poirot
The title is the clue bugatti.

Assuming you mean e^(xy), then you want d/dx(xy)*e^(xy).
Indeed. Whenever I see the phrase "implicit differentiation", I assume that we're considering one variable to be a function of the other.

6. Originally Posted by poirot
The title is the clue bugatti.

Assuming you mean e^(xy), then you want d/dx(xy)*e^(xy).
No I was referring to sin (xy) but thanks anyway!

7. Originally Posted by jimbowickersmack
sin(xy)=e^xy

should i use product or chain rule on the left side of the equation? I just started doing these and I am a bit confused. Thanks for any help
BOTH. Use the chain rule write d sin(xy)/dx= cos(xy) d(xy)/dx, then use the product rule to find d(xy)/dx.