Differentiation Flashcards
1
Q
Exponentials & Logarithms
dy/dx [e^kx] =
A
ke^kx
2
Q
Exponentials & Logarithms
dy/dx [a^kx] =
A
a^kx(k ln a)
3
Q
Exponentials & Logarithms
dy/dx [ln x] =
A
1/x
4
Q
Chain Rule
dy/dx =
A
dy/du x du/dx
y = function of u
u = another function of x
5
Q
Chain Rule
if y = [f(x)]^n then dy/dx =
A
n[f(x)]^n-1 x f’(x)
6
Q
Chain Rule
if y = f[g(x)] then dy/dx =
A
f’[g(x)] x g’(x)
7
Q
Chain Rule
if function isnt in the form y = f(x), dy/dx =
A
1 / dx/dy
8
Q
Product Rule
dy/dx =
A
uv’ + vu’
9
Q
Quotient Rule
dy/dx =
A
vu’ - uv’ / v^2
10
Q
Trigonometric Functions
dy/dx [TAN kx] =
A
kSEC^2 kx
11
Q
Trigonometric Functions
dy/dx [COSEC kx] =
A
-kCOSEC kx COT kx
12
Q
Trigonometric Functions
dy/dx [COT kx] =
A
-kCOSEC^2 kx
13
Q
Trigonometric Functions
dy/dx [SEC kx] =
A
kSEC kx TAN kx
14
Q
Parametric
dy/dx =
A
dy/dt / dx/dt
15
Q
Implicit
dy/dx [f(y)] =
A
f’(y) dy/dx
