# Thread: derivatives exponential functions

1. ## derivatives exponential functions

could someone please tell me step by step how to solve this equation?Because i am completely lost.

Find dy/dx for e^xy+x^2-y^2=10

2. Originally Posted by geryuu
could someone please tell me step by step how to solve this equation?Because i am completely lost.

Find dy/dx for e^xy+x^2-y^2=10

Implicit differentiation (derive each term both according to x and to y):

e^xy + x^2 - y^2 = 10 ==> ye^xy dx + xe^xy dy + 2x dx - 2y dy = 0

==> (ye^xy + 2x)dx = (2y - xe^xy)dy ==>

dy/dx = (ye^xy + 2x)/(2y - xe^xy)

Tonio

3. Use $\frac{dy}{dx} = \frac{-F_x}{F_y}
$

Do you know how to find $F_x$ and $F_y$ ?