Differentiation Cards

Question 1

simplifying e^x e^y

Answer 1

e^x+y

Question 2

simplifying 1/e^x

Answer 2

e^-x

Question 3

simplifying (e^x)^y

Answer 3

e^xy

Question 4

simplifying ln(xy)

Answer 4

lnx + lny

Question 5

simplifying ln(x/y)

Answer 5

lnx - lny

Question 6

simplifying ln(x^y)

Answer 6

y lnx

Question 7

simplifying ln(e^A)

Answer 7

A

Question 8

what is the chain rule

Answer 8

d/dx u(v(x)) = dv/dx * du/dv

Question 9

what is the product rule

Answer 9

d/dx (u(x) v(x)) = (du/dx) v + u(dv/dx)

Question 10

differential of kx^n

Answer 10

n kx^ n-1

Question 11

differential of Ae^kx

Answer 11

kAe^kx

Question 12

differential of sin

Answer 12

cos

Question 13

differential of cos

Answer 13

-sin

Question 14

differential of Alnkx

Answer 14

A/x (note k has disappeared)

Question 15

differential of lnx

Answer 15

1/x

Question 16

differential of Ae ^-nx

Answer 16

-n Ae ^-nx

Question 17

differential of A/X^n

Answer 17

-nA/x^n+1

Question 18

differential of 3q^4

Answer 18

12q^3

Question 19

differential of 3lnq

Answer 19

3/q

Question 20

integral of k

Answer 20

kx + c

Question 21

integral of kx^n

Answer 21

(k/n+1) * x^n+1 + c

Question 22

integral of Ae^kx

Answer 22

1/k Ae^kx + c

Question 23

integral of sin

Answer 23

-cos

Question 24

integral of cos

Answer 24

sin

Question 25

integral of 1/x

Answer 25

lnx + c = lnB

where B = e^c

Question 26

integral of 5x^4

Answer 26

x^4+1 / 4+1 = 5 (x^5/5) = x^5

Question 27

For the chain and product rules what is important to know about v and u?

Answer 27

they are UNDIFFERENTIATED when subbed in at the end

Question 28

what is the difference between partial and full differentiation?

Answer 28

partial = whatever isn’t in the d/d(?) is left as constant so not written in the answer

full = e.g. dy/dx both x and y are differentiated

Question 29

what is the conversion from ln to log?

Answer 29

ln = 0.0592 log