Differentiation 2

Question 1

what is the differentiation of a^x

Answer 1

a^x ln(a)

Question 2

whats the product rule for y = uv

Answer 2

dy/dx = uv’ + vu’

Question 3

whats the quotient rule for y = u/v

Answer 3

dy/dx = (vu’ - uv’) / v^2

Question 4

whats the differentiation of tanx

Answer 4

sec^2x

Question 5

how would you work out the differentiations of cosecx, secx and cotx in an exam

Answer 5

by looking in the formula book dumbass

Question 6

what does an equation that needs to be implicitly differentiated look like

Answer 6

it has x and y on both sides of the equation that cant be simplified out or separated

Question 7

what is the first step to implicitly differentiate

Answer 7

put a d/dx next to every term

Question 8

what is the second step to implicitly differentiate

Answer 8

differentiate only the x terms and constants (nothing with a y next to it)

Question 9

what is the third step to implicitly differentiate

Answer 9

only differentiate the y terms (dont do ones with a xy combination)

Question 10

how would you do it

Answer 10

• you do this just be normally differentiating the y in terms of y
• then sticking it next to a dy/dx

Question 11

what is the fourth step to implicitly differentiate

Answer 11

use the product rule to differentiate the xy combination

Question 12

how would you do it

Answer 12

• when differentiating y with respects to x
• just write it as dy/dx
• other than that use the product rule as normal

Question 13

what is the final step to implicitly differentiate

Answer 13

rearrange the equation for dy/dx