differentiation

Question 1

how is the gradient of a curve shown?

Answer 1

an expression in terms of x (gradient function)

Question 2

formula for the gradient of a curve at a specific point (x)

Answer 2

lim h = f(x+h) - f(x)
/ h (where H is so small it is negligible)

Question 3

how do you differentiate X^n

Answer 3

if y=ax^n then dy/ dx = nax^(n-1)

(multiply x by the power and reduce the power by 1
eg. y=x^4 = 4x^3