In this page normal using differentiation we are going to see the how to find equation of normal using the concept differentiation.

Procedure of finding equation of normal using differentiation :

**Step 1 :** Differentiate the given equation of the curve once.
If we differentiate the given equation we will get slope of the curve
that is slope of tangent drawn to the curve.

**Step 2 : **We have to apply the given points in the general slope to get slope of the particular tangent at the particular point.

**Step 3 :** From slope of tangent we have to find the slope of normal (-1/m).

**Step 4 :** Now we have to apply the point and the slope in the formula

(y - y₁) = (-1/m) (x - x₁)

Now we are going to see some example problems to understand this concept.

**Example 1:**

Find the equation of the tangent to the curve y = x³ at the point (1,1)

**Solution:**

y = x³

Step 1 : Differentiate the equation of the curve once to find the slope of the curve that is slope of the tangent drawn to the curve.

dy/dx = 3 x²

slope of the curve at the point (1 , 1)

dy/dx = 3 (1)²

slope of the curve that is lope of tangent at the point (1,1) dy/dx = 3

slope of normal = -1/3

**Equation of the normal :**

(y - y₁) = (-1/m) (x - x₁)

(y - 1) = (-1/3) (x - 1)

3 (y - 1) = -1 (x - 1)

3 y - 3 = - x + 1

x + 3 y - 3 - 1 = 0

x + 3 y - 4 = 0

**Example 2:**

Find the equation of normal to the curve y = x² - x - 2 at the point (1,-2)

**Solution:**

y = x² - x - 2

Step 1 : Differentiate the equation of the curve once to find the slope of the curve that is slope of the tangent drawn to the curve.

dy/dx = 2 x - 1

slope of the curve that is slope of the tangent at the point (1 , -2)

dy/dx = 2 (1) - 1

= 2 - 1

= 1

slope of the tangent (dy/dx) = 1

slope of normal = -1/1

= -1

**Equation of the normal:**

(y - y₁) = (-1/m) (x - x₁)

(y - (-2)) = -1 (x - 1)

y + 2 = - x + 1

x + y + 2 - 1 = 0

x + y + 1 = 0

normal using differentiation

- Equation of tangent
- First Principles
- Implicit Function
- Parametric Function
- Substitution Method
- logarithmic function
- Product Rule
- Chain Rule
- Quotient Rule
- Rolle's theorem
- Lagrange's theorem
- Finding increasing or decreasing interval
- Increasing function
- Decreasing function
- Monotonic function
- Maximum and minimum
- Examples of maximum and minimum