Unit 1

Question 1

What does sin x differentiate to?

Answer 1

Cos x

Question 2

What does cos x differentiate to?

Answer 2

-Sin x

Question 3

What does tan x differentiate to?

Answer 3

2

sec x

Question 4

What does cosec x differentiate to?

Answer 4

• cosec x Cot x

Question 5

What does sec x differentiate to?

Answer 5

Sec x Tan x

Question 6

What does cot x differentiate to?

Answer 6

2

-cosec x

Question 7

why is sinx/cosx equal to?

Answer 7

tan x

Question 8

what is 1/sin x equal to

Answer 8

cosec x

Question 9

what is 1/cos x equal to

Answer 9

sec x

Question 10

what is 1/tan x equal to

Answer 10

cos x/ sin x = cot x

Question 11

-1

What does sin x differentiate to?

Answer 11

2
1/✔️1-x

✔️ = square root

Question 12

• 1

What does cos x differentiate to?

Answer 12

2
-1/✔️1-x

✔️ = square root

Question 13

-1

What is the does tan x differentiate to?

Answer 13

2

1/1+x

Question 14

What is the product rule

Answer 14

Y = UV

dy/dx = U’V + UV’

Question 15

What is the quotient rule

Answer 15

y = u/v
2
dy/dx = U’V-UV’/V

Question 16

What does. 2. differentiate to
x
e

Answer 16

2
x
2x e

Question 17

how do you differentiate exponential

Answer 17

you times the exponential by the derivative of the power while the power remains constant

 Ex/
     3   
   x
 e
becomes

       3
2. x 3x e

Question 18

how do you differentiate natural logs

ln x

Answer 18

1 is divided by the x part and then times by the differentiation of it

Ex/ ln 3x - 1

=. 1/3x - 1 times by 3
=. 3/3x - 1

Question 19

how do you differentiate implicitly

Answer 19

you differentiate the y normally (as if it was an x) then you add a dy/dx after it

Ex/. 2
d/dx y. = 2y dy/dx
3. 2
d/dx. y. = 3y. dy/dx

d/dx. sin x = cos x dy/dx

      y.         y d/dx e.   =.  e  dy/dx

d/dx ln y =. 1/y. dy/dx

Question 20

how do you implicitly differentiate the equation of a tangent

Answer 20

differentiate implicitly then rearrange so you have a dy/dx = equations
then sub in the values for x and y ( given by the coordinates in the question)
this gives the gradient of the tangent (m)

sub these values into y-b = mx-a ( with the y coordinated being b and the x coordinate being a) to get the equations of the tangent

Question 21

what are the log rules

Answer 21

ln ab = ln a + ln b

ln a/b = ln a - ln b

  n ln a    = n ln a

Question 22

how do you logarithmicly differentiate

Answer 22

take a natural log of both sides, you then simplify through the log rules and differentiation

Question 23

what is the formula for parametric differentiation

Answer 23

dy/dt
dy/dx = ———
dx/dt

Question 24

how do you parametrically differentiate

Answer 24

differentiate the x term
differentiate the y term
you then put them together through the parametric differentiation equation [ (dy/dt)/(dx/dt) ]
this gives you your final equation

Question 25

how’s do you integrate exponentials

Answer 25

integrated normally but decide by the derivative of the power of the exponential

Ex

       3x+2    f.   e.          dx

        3x+2 =. 1/3e.          + c

Question 26

how do you standard integrate with the chain rule

Answer 26

add one to the power of equation, divide by that then divide by the derivative of the equation

Ex/
                     4
      f  (3x +2 ).  dx
                                   5
= 1/5 X 1/3 X (3x +2 )   + c

                     5 = 1/15. (3x +2 ).   + c

Question 27

How do you integrate logs

Answer 27

You change the 1/x back into the ln | x | ( making sure to have vertical lines in the ln ) then divide by the derivative of the x

Ex/

f 1/9x + 5 dx

= 1/9 ln | 9x + 5 | + c

Question 28

what is the formula for integration by parts

Answer 28

f U V’ = U V - f U’ V

Question 29

what is an example of integration by parts

Answer 29

I = f x sin3x dx

u = x.     v’ = sin3x 
u’ = 1     v = -1/3 cos3x

I = uv - f u’v dx
I = -1/3 x cos3x - f -1/3 cos3x dx
I = -1/3 x cos3x + f 1/3 cos3x dx
I = -1/3 x cos 3x + 1/3 X 1/3 X sin 3x + c
I = -1/3 x cos 3x + 1/9 sin 3x + c