Derivatives and Rules of Differentiation

Question 1

Derivative

Answer 1

The rate of change of a function f at point x (i.e. its gradient)

Question 2

How is a derivative written?

Answer 2

f’(x) or fd/dx

Question 3

Calculating the derivative

Answer 3

(f (x + Δ) - f (x)) / Δ

Question 4

Differentiation

Answer 4

The derivative of a function at all points

Question 5

If f is a constant function, then…

Answer 5

c’ = 0

Question 6

If f(x) = x, then…

Answer 6

x’ = 1

Question 7

If f(x) = x^n, where n is constant, then…

Answer 7

x^n’ = nx^(n-1)

Question 8

If f(x) = c*g(x), where c is constant, then…

Answer 8

(c * g)’ = c * g’

Question 9

If f(x) = g(x) ± h(x) then…

Answer 9

(g ± h)’ = g’ ± h’

Question 10

If f(x) = g(x) * h(x) then…

Answer 10

(g * h)’ = g’ * h + g * h’

Question 11

If f(x) = g(x) / h(x) then…

Answer 11

(g / h)’ = (g’ * h - g * h’) / h^2

Question 12

If f(x) = h(g(x)) then…

Answer 12

(h(g(x)))’ = g’(x) * h’(g(x))

Question 13

Minima/maxima

Answer 13

The points in a graph where the direction changes

Question 14

How do you find the slope of a line?

Answer 14

Calculate the derivative at the specified point

Question 15

Local minima/maxima

Answer 15

Points in a line where the curve is stationary

Question 16

f’(x) = 0

Answer 16

The stationary points in the graph

Question 17

Points of inflexion

Answer 17

Stationary points that aren’t local min/max points