# GRE Subject Test: Math : Implicit Differentiation

## Example Questions

### Example Question #1 : Partial Differentiation

Differentiate the following with respect to

Explanation:

The first step is to differentiate both sides with respect to :

Note: Those that are functions of  can be differentiated with respect to , just remember to mulitply it by

Now we can solve for :

### Example Question #2 : Partial Differentiation

Find

for .

Explanation:

Our first step would be to differentiate both sides with respect to :

The functions of  can be differentiated with respect to , just remember to multiply by  .

### Example Question #126 : Calculus

Differentiate the following to solve for .

Explanation:

Our first step is to differentiate both sides with respect to :

The functions of  can by differentiated with respect to , just remember to multiply them by

### Example Question #3 : Partial Differentiation

Differentiate the following with respect to .

Explanation:

Our first step is to differentiate both sides with respect to :

Note: we can differentiate the terms that are functions of  with respect to , just remember to multiply it by .

Note: The product rule was applied above: