Differentiation Flashcards
(18 cards)
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
What is coskx differentiated?
-ksinkx
What is tankx differentiated?
Ksec^2kx
What is lnkx differentiated?
1/x
