# What is the slope of the tangent line of #x^3-(xy)/(x-y)= C #, where C is an arbitrary constant, at #(1,4)#?

##### 1 Answer

The slope is

#### Explanation:

Given that

So the curve we are being asked about has equation:

Simplifying gets us the equation:

Note that this equation is linear in

(If you're serious about learning mathematics, try solving for

Differentiating implicitly gets us:

Rather than solving algebraically first, I think it is simpler to substitute the values now.

(Again, trying the other order --solving for

At

Do the artihmetic/algebra to get