Differentiation

Question 1

What does dy/dx show?

Answer 1

the rate of change of y with regards to x

the gradient of a line

Question 2

How do you find dy/dx?

Answer 2

multiply each x value by it’s power, then subtract 1 from the power and write it out:

3x[3] becomes 9x[2]

values of x without a power become the value without the x

numbers without an x value become 0

Question 3

What should you do before differentiating?

Answer 3

rearrange the equation into powers of x

Question 4

What do you do if an equation has an x value divided by a whole value?

Answer 4

x/2 = 1/2x

x/3 = 1/3x

etc.

Question 5

What do you do if there is an x value on the bottom of a fraction?

Answer 5

it becomes negative and is multiplied by the top part

if there is a power it becomes to the negative power

Question 6

using differentiation to find a gradient

Answer 6

substitute the x value into the dy/dx equation

Question 7

finding the equation of the tangent of a curve

Answer 7

use differentiation to find the gradient

using y = mx + c and the same x and y coordinates find c

Question 8

finding the equation of the normal to a tangent

Answer 8

the normal is just a line perpendicular to the tangent

the gradient will be the negative reciprocal of the tangent

substitute x and y values to find the equation

Question 9

using differentiation to find a point where the gradient is certain value

Answer 9

set dy/dx as the gradient equal to the equation

solve for x and substitute back into the suitable equation

Question 10

stationary points

Answer 10

where the gradient equals 0