# How to find the equation of the tangent and the normal of this curve?

##### 1 Answer

#### Answer:

Tangent line is:

Normal to this is:

#### Explanation:

In order to find the equation of the tangent line, we must first find the gradient of this line at the given point.

We can do this by finding the gradient function of

The gradient function is generally called the derivative:

To differentiate our function we need to use the Chain Rule.

If we let

Then:

This now means

The chain rule states that:

I will do this step by step so you can see how it comes together.

First:

But

So:

Second:

We now multiply these:

We have the point

We know

If two lines are perpendicular then the products of their gradients is

Let gradient of the normal to the line be

So we know the gradient of the normal and we also know it passes through the point

Tangent line is:

Normal to this is:

GRAPH: