Differentiation Flashcards
What does concave mean?
In curves inwards
What does convex mean?
It curves outwards
What does it mean if the second derivative is above zero?
It is a minimum and is an increasing gradient so concave upwards
What does it mean if the second derivative is below zero?
The gradient is decreasing so it is a maximum and concave downwards
What does it mean if the second derivative is zero?
The point could be either a point of inflection, a minimum or a maximum
Where the curve changes from concave downwards to concave upwards
When do you use the product rule?
When you want to differentiate 2 functions multiplied together
What is the product rule?
(F(x)g(x))’=f(x)g’(x) + g(x)f’(x)
When do you use the quotient rule?
To differentiate 2 functions divided by each other
What is the quotient rule?
(F(x)/g(x))’=g(x)f’(x)-f(x)g’(x)/g(x)^2
When would you use the chain rule?
To differentiate a function of a function
What is the chain rule?
(F(g(x)))’=f’(g(x))g’(x)
Differentiate outside x differentiate inside
If y=f(g(x)) let u=g(x) then y=f(u)
dy/dx= dy/du x du/dx
How do you calculate rate of change?
Change in something/ change in time
What to do if you are asked to find dx/dy?
Differentiate as normal the just invert put it under one
What is e^kx differentiated?
Ke^kx
What is sinkx differentiated?
Kcoskx
