# How do you find the derivative of # e^(xy)=x/y#?

##### 1 Answer

Use the natural log on both side, separate the division into the difference of two logs, use the product rule on the left and the chain rule on the y terms.

#### Explanation:

Use the natural logarithm on both sides:

The inverse functions on the left cancel each other:

Division in the argument of a logarithm is the same as the difference between the dividend and the divisor:

Add #ln(y) to both sides:

Differentiate each term:

Use the product rule combined with the chain rule on the first term:

Use the chain rule on the second term:

The last term is trivial:

Subtract y from both sides:

Factor out

Make common denominators on both sides:

Multiply both sides by

Use the distributive property on the numerator and denominator: