differentiation

Question 1

Chain rule eqn

Answer 1

(dy/dx) = (du/dx) x (dy/du)

Question 2

Product rule eqn

Answer 2

(dy/dx) = u(dv/dx) + v(du/dx)

Question 3

Quotiant rule eqn

Answer 3

(dy/dx) = (v(du/dx) - u(dv/dx)) / v^2

Question 4

y=sinf(x)

Answer 4

dy/dx = f’(x)cosf(x)

Question 5

y=cosf(x)

Answer 5

dy/dx = -f’(x)sinf(x)

Question 6

dy/dx =

Answer 6

1 / (dx/dy)

Question 7

y=lnf(x)

Answer 7

dy/dx = f’(x) / f(x)

Question 8

y=e^f(x)

Answer 8

dy/dx = f’(x)e^f(x)

Question 9

y=tanf(x)

Answer 9

dy/dx = f’(x)sec^2f(x)

Question 10

y=cotf(x)

Answer 10

dy/dx = -f’(x)cosec^2f(x)

Question 11

y=secf(x)

Answer 11

dy/dx = f’(x)secf(x)tanf(x)

Question 12

y=cosecf(x)

Answer 12

dy/dx= -f’(x)cosecf(x)cotf(x)

Question 13

y=a^f(x)

Answer 13

dy/dx =a^f(x)f’(x)ln(a)

Question 14

what assumptions can be made when differentiating sin and cos from 1st principles

Answer 14

sin(h)/h > 1
sin(h)/ h tends to 1

(cos(h)-1)/h >0
(cos(h)-1)/h tends to 0

Question 15

Rules when differentiating sin(5x) from first principles

Answer 15

Set out this question as lim sin5(x+h)-sin(5x) / h
h>0
when doing this sin(ah)/h > a rarther than 1.
In this example sin(5h)/h >5