Differentiation

Question 1

What is the formula for differentiation of first principles?

Answer 1

Question 2

What do we say when f’(x) <0?

Answer 2

The function is decreasing

Question 3

What do we say when f’(x)=0?

Answer 3

The function is stationery

Question 4

What do we say when f’(x)>0?

Answer 4

The function is increasing

Question 5

What do we say when f’‘(x)<0?

Answer 5

It is concave/ corresponds with a maximum point.

Question 6

What do we say when f’‘(x)=0

Answer 6

It is a point of inflection

Question 7

What does it mean when f’‘(x)>0?

Answer 7

It is convex/corresponds to a minimum point

Question 8

How will this function differentiate?

Answer 8

Question 9

How will this function differentiate?

Answer 9

Question 10

How will this function differentiate?

Answer 10

Question 11

How will this function differentiate?

Answer 11

Question 12

How will this function differentiate?

Answer 12

Question 13

How will this function differentiate?

Answer 13

Question 14

What is the fast way to differentiate using the chain rule?

Answer 14

1. Differentiate the bracket
2. Multiply the first derivative by the power and the coefficient to get your new coefficient
3. Leave the bracket as normal
4. Decrease the power by 1

Question 15

What is the normal formula for differentiating using the chain rule?

Answer 15

Set the function in the bracket as u

Question 16

What are the steps to differentiate using the product rule?

Answer 16

1. Split the function into u and v
2. Differentiate u and v
3. Multiply u and v’, then u’ and v
4. Add them together

Question 17

What are the steps for differentiating using the quotient rule?

Answer 17

1. Split the function into u and v
2. Differentiate u and v
3. Multiply u and v’, then u’ and v
4. vu’-uv’ divided by v^2

Question 18

What does ‘rate’ mean?

Answer 18