Differentiation Cards Flashcards
1
Q
simplifying e^x e^y
A
e^x+y
2
Q
simplifying 1/e^x
A
e^-x
3
Q
simplifying (e^x)^y
A
e^xy
4
Q
simplifying ln(xy)
A
lnx + lny
5
Q
simplifying ln(x/y)
A
lnx - lny
6
Q
simplifying ln(x^y)
A
y lnx
7
Q
simplifying ln(e^A)
A
A
8
Q
what is the chain rule
A
d/dx u(v(x)) = dv/dx * du/dv
9
Q
what is the product rule
A
d/dx (u(x) v(x)) = (du/dx) v + u(dv/dx)
10
Q
differential of kx^n
A
n kx^ n-1
11
Q
differential of Ae^kx
A
kAe^kx
12
Q
differential of sin
A
cos
13
Q
differential of cos
A
-sin
14
Q
differential of Alnkx
A
A/x (note k has disappeared)
15
Q
differential of lnx
A
1/x
16
Q
differential of Ae ^-nx
A
-n Ae ^-nx
17
Q
differential of A/X^n
A
-nA/x^n+1
18
Q
differential of 3q^4
A
12q^3
19
Q
differential of 3lnq
A
3/q
20
Q
integral of k
A
kx + c
21
Q
integral of kx^n
A
(k/n+1) * x^n+1 + c
22
Q
integral of Ae^kx
A
1/k Ae^kx + c
23
Q
integral of sin
A
-cos
24
Q
integral of cos
A
sin
25
integral of 1/x
lnx + c = lnB
where B = e^c
26
integral of 5x^4
x^4+1 / 4+1 = 5 (x^5/5) = x^5
27
For the chain and product rules what is important to know about v and u?
they are UNDIFFERENTIATED when subbed in at the end
28
what is the difference between partial and full differentiation?
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
29
what is the conversion from ln to log?
ln = 0.0592 log
