Derivatives Flashcards
1
Q
d/dx (sin(x))
A
cos(x)
2
Q
d/dx (cos(x))
A
-sin(x)
3
Q
d/dx (sin(ax+b))
A
acos(ax+b)
4
Q
d/dx (cos(ax+b))
A
-asin(ax+b)
5
Q
d/dx (sin(x°))
A
π/180 cos(x°)
6
Q
d/dx (cos(x°))
A
-π/180 sin(x°)
7
Q
d/dx (sin(f(x)))
A
f’(x)cos(f(x))
8
Q
d/dx (cos(f(x)))
A
-f’(x)sin(f(x))
9
Q
d/dx (tan(x))
A
1+tan^2(x)=1/cos^2(x)=sec^2(x)
10
Q
d/dx (ln(x))
A
1/x
11
Q
d/dx (ln(f(x)))
A
f’(x)/f(x)
12
Q
d/dx (e^x)
A
e^x
13
Q
d/dx (e^f(x))
A
f’(x)e^f(x)
14
Q
What is the chain rule
A
If y=f(u) and u = g(x), then
dy/dx=y’*u’
15
Q
What is the product rule
A
If y=f(u)f(v), then
dy/dx=uv’+v*u’
16
Q
What is the quotient rule
A
If y=f(u)/f(v), then
dy/dx=(vu’-uv’)/v^2
