implicit differentiation help

[bassprosox]

ive been trying to figure out how to differentiate x(e^z)+z(e^y)=x+y in terms of x and y to find dz/dx?
anyone know where to go with this? Thanks

 

[royhaas]

Use the chain rule.

 

[JuicyBurger]

\(\displaystyle x(e^z)+z(e^y)=x+y\) in terms of x and y to find dz/dx

\(\displaystyle e^z + xe^z+e^yz' = 1\)

Just differentiate both x and z similar to if they were all the same variable. Make sure when you take the derivative of z that you put z', since z is a function.

Solve for z'

 

[BigGlenntheHeavy]

\(\displaystyle JuicyBurger, \ shouldn't \ that \ be:\)

\(\displaystyle e^{z}+xe^{z}z'+e^{y}z'=1\)

\(\displaystyle Then \ \frac{dz}{dx} \ = \ -\frac{e^{z}-1}{xe^{z}+e^{y}}.\)