P- Differentiation (quadratics) ED

Question 1

What is the differentiation formula when y=ax?

Answer 1

dy/dx = (na)x power of n-1

Question 2

How do you get 1/a to the power of m out of a fraction?

Answer 2

Becomes 1am to the power of -1
(Multiply top and bottom, to the power of negative n)

Question 3

What are 4 things to do when differentiating harder expressions?

Answer 3

1) Turn roots into powers
2) Split up fractions
3) Expand brackets out
4) Beware of numbers in denominators

Question 4

How do you differentiate from 1st principles?

Answer 4

1) Make a new coordinate with +h added on to original coordinate numbers
2) Put the coordinates into Δy / Δx
3) Simplify till all h’s are gone and you have a gradient

Question 5

What goes to the left of the equation when differentiating from 1st principles?

Answer 5

lim
h→0

Question 6

How do you find an equation of a tangent?

Answer 6

1) Get gradient by subbing x value into differentiated equation
2) Work out y value by subbing x into original equation
3) Sub all values into y-y1=m(x-x1)

Question 7

What is an increasing function?

Answer 7

When the gradient is at least 0
f’(x)≥0 for all x values

Question 8

What is a strictly increasing function?

Answer 8

When the gradient is greater than 0
f’(x)>0 for all x values

Question 9

What is a decreasing function?

Answer 9

When the gradient is less than 0
f’(x)<0