# How do you use implicit differentiation to find dy/dx given #2^sqrt(xy)=x#?

##### 2 Answers

#### Explanation:

Differentiate both members of the equation with respect to

Substitute

Solving for

Now note that:

and so:

Substituting in the expression of

You can also first make

Obtaining naturally the same result.

x and y > 0.

#### Explanation:

graph{x-2^sqrt(xy)=0x^2 [-39.94, 39.94, -19.96, 19.98]} To make the function real,

Using logarithmic differentiation,