What is the formula for differentiation of first principles?
What do we say when f’(x) <0?
The function is decreasing
What do we say when f’(x)=0?
The function is stationery
What do we say when f’(x)>0?
The function is increasing
What do we say when f’‘(x)<0?
It is concave/ corresponds with a maximum point.
What do we say when f’‘(x)=0
It is a point of inflection
What does it mean when f’‘(x)>0?
It is convex/corresponds to a minimum point
How will this function differentiate?
How will this function differentiate?
How will this function differentiate?
How will this function differentiate?
How will this function differentiate?
How will this function differentiate?
What is the fast way to differentiate using the chain rule?
- Differentiate the bracket
- Multiply the first derivative by the power and the coefficient to get your new coefficient
- Leave the bracket as normal
- Decrease the power by 1
What is the normal formula for differentiating using the chain rule?
Set the function in the bracket as u
What are the steps to differentiate using the product rule?
- Split the function into u and v
- Differentiate u and v
- Multiply u and v’, then u’ and v
- Add them together
What are the steps for differentiating using the quotient rule?
- Split the function into u and v
- Differentiate u and v
- Multiply u and v’, then u’ and v
- vu’-uv’ divided by v^2
What does ‘rate’ mean?
