# Thread: find the equation of a tangent line (calc)

1. ## find the equation of a tangent line (calc)

Hey guys!
Here's a question on a math test (with solutions) that I don't understand very well:

So for the first step, i understand what they did, and how they got the point on the graph.

For the second step, i see they pulled out $4x$ and i understand how they get $3y^2y'$ but i dont understand how they got $4y^3$ and $15y^2y'$

could anyone help me with that?

2. $4xy^3 + 27 = 5y^3$

Using implicit differentiation, 4xy^3 becomes:

$4x\cdot 3y^2 y' + y^3\cdot 4 = 12xy^2y' + 4y^3$

Differentiating 5y^3:

$5(3y^2)y' = 15y^2y'$

Is this okay?

3. yes! thanks, i get it!