Differentiation: Tangent and Normal

A tangent is a line that touches the curve.

A normal is a line that is perpendicular to the normal.

Remember this formula:
(gradient of tangent) x (gradient of normal) = -1

How to find gradient of tangent at x = a?
1) Differentiate y (find dy/dx)
2) substitute x = a into dy/dx to find gradient of tangent.

How to find gradient of normal at x = a?
1) Differentiate y (find dy/dx)
2) substitute x = a into dy/dx to find gradient of tangent.
3) find gradient of normal by using the following formulae: -1 / (gradient of tangent)

How to find equation of tangent at x = a?
1) Differentiate y (find dy/dx)
2) substitute x = a into dy/dx to find gradient of tangent. Let's call it m1.
3) substitute x into the y equation, to get a y value. Let's call this y value y1.
4) equation of equation : y -y1 = m1(x-a)

How to find equation of tangent at x = a?
1) Differentiate y (find dy/dx)
2) substitute x = a into dy/dx to find gradient of tangent. Let's call it m1.
3) substitute x into the y equation, to get a y value. Let's call this y value y1.
4) equation of equation : y -y1 = m1(x-a)

How to find equation of normal at x = a?
1) Differentiate y (find dy/dx)
2) substitute x = a into dy/dx to find gradient of tangent. Let's call it m1.
3) Find gradient of normal by using the formula gradient of normal = -1/ (gradient of tangent).
Let's call this gradient of normal m2.
3) substitute x into the y equation, to get a y value. Let's call this y value y1.
4) equation of equation : y -y1 = m2(x-a)