# How do you differentiate #4xy-3x-11=0#?

##### 2 Answers

#### Explanation:

Assume the equation

Now solve for

If you happen to know a specific point

The particular equation

Now we can differentiate this in the ordinary way to get

It is the same!

As an example of a point on this curve, we can use the equation

The equation of the tangent line to the curve at that point is therefore

Here's a graph of the situation just described:

Assuming that we want to find

Using implicit differentiation, we get:

Solving for

#### Explanation:

The question is posted under "Implicit Differentiation", so let's do it that way first:

**Leaving the function Implicit**

In order to differentiate

Remember that we are assuming that

the derivative is:

Back to this problem:

**Making the function explicit**

Solve

We could differentiate using the quotient rule, but it is perhaps simpler to rewrite again:

# = 3/4 +11/4x^-1#

So

# = -11/(4x^2)#

**The answers are equivalent**

To see that the answer are equivalent compare:

with

Using Implicit differentiation, there is still a

# = (3-(3x+11)/x)/(4x)#

# = (3x-3x-11)/(4x^2)#

# = -11/(4x^2)#