# High School Calculus/Implicit Differentiation

### Implicit Differentiation[edit]

When a functional relation between ** x** and

**cannot be readily solved for**

*y***, the preceding rules may be applied directly to the implicit function.**

*y*The derivative will usually contain both ** x** and

**. Thus the derivative of an algebraic function, defined by setting the polynomial of**

*y***and**

*x***to zero.**

*y*

**Ex. 1**

Given the function *y* of *x*

Find

Since

In solving for we must first factor the differentiation problem

In doing this we get

From here we subtract the to one side

Thus giving us

Here I am going to skip a step in solving this implicit differentiation problem. I am going to skip the step where I divide the -1 over to the other side.

From here we divide the polynomial from the over to the other side. Giving us

Now we simplify and get

**Other problems to work on**

**Ex. 2**

Find given the function

**Ex. 3**

Find given the function