A1) Differentiation from first principal- A and B are the two point on a curve representing small increment in the x and y directions respectively. Gradient of chord- However- Hence- Here When determining the gradient of a tangent to a curve there are two notations used. The gradient of the curve at A can either be written as,
Where Or we can write it as- |

A2) We know that- Here Substituting ( Hence- |
f(x) | dy/dx |
Sin ax | a cos ax |
Cos ax | -a sin ax |
Log ax | 1/x |





The given function can be written in the form Now- Differentiation of a product- When y = uv and u, v are both function of x- then
Differentiation of a quitient- When y = u/v and u,v are the functions of x- Then- |


































Let y = f(x) = Then the first derivative will be- Putting By using middle term splitting- We get- Now we will find the second derivative- We get- Here At x = 4, At x = 16, |