9: Differentiation Flashcards
1
Q
What is the result when you differentiate sin(x)?
A
cos(x)
2
Q
What is the result when you differentiate cos(x)?
A
-sin(x)
3
Q
Differentiate sin(x) from first principles.
A
4
Q
Differentiate cos(x) from first principles.
A
5
Q
y = sin(kx)
dy/dx =
A
kcos(kx)
6
Q
y = cos(kx)
dy/dx =
A
-ksin(kx)
7
Q
y = ekx
dy/dx =
A
kekx
8
Q
y = ln(x)
dy/dx =
A
1/x
9
Q
y = ln(kx)
dy/dx =
A
y = ln(kx) = ln(k) + ln(x)
ln(k) is a constant
dy/dx = 1/x
10
Q
y = akx
dy/dx =
A
akxk ln(a)
11
Q
y = akx and dy/dx = akx kln(a)
When is this true?
A
K ϵ ℝ, a > 0
12
Q
Show that the derivative of ax is axln(a)
A
y = ax
ln(y) = ln(ax) = xln(a)
y = exln(a)
Where y = ekx, dy/dx = kekx
dy/dx = ln(a) exln(a) = ln(a) eln(a^x)
= ln(a) ax = ax ln(a)