# Thread: Derivation of n functions

1. ## Derivation of n functions

Calculate

1) $z=e^\frac{s}{t}$, $s=xy^2$ and $t=5x+2y^3$. Calculate $\frac{dz}{dx}$ and $\frac{dz}{dy}$

My solution:

$\frac{dz}{dx} = \frac{dz}{ds} \frac{ds}{dx} + \frac{dz}{dt} \frac{dt}{dx}$

$\frac{dz}{dx}= \frac{y^2e^\frac{s}{t}}{t}-\frac{5se^\frac{s}{t}}{t^2}$

The answer is correct?

$\frac{dz}{dy} = \frac{2xye^\frac{s}{t}}{t}-\frac{6yse^\frac{s}{t}}{t^2}$????

2. Originally Posted by Apprentice123
Calculate

1) $z=e^\frac{s}{t}$, $s=xy^2$ and $t=5x+2y^3$. Calculate $\frac{dz}{dx}$ and $\frac{dz}{dy}$

My solution:

$\frac{dz}{dx} = \frac{dz}{ds} \frac{ds}{dx} + \frac{dz}{dt} \frac{dt}{dx}$

$\frac{dz}{dx}= \frac{y^2e^\frac{s}{t}}{t}-\frac{5se^\frac{s}{t}}{t^2}$

The answer is correct? Yes.

$\frac{dz}{dy} = \frac{2xye^\frac{s}{t}}{t}-\frac{6yse^\frac{s}{t}}{t^2}$???? y should be y^2 in the second fraction. Otherwise it's correct.
And of course all the d's should be partial d's (\partial in LaTeX).

3. thank you