TOPIC 11: DIFFERENTIATION Flashcards
Differentiation of trigonometric functions
sin x = cos x
cos x = - sin x
tan x = sec² x
Differentiation of sec / cosec / cot
sec x = sec x tan x
cosec x = - cosec x cot x
cot x = - cosec² x
Differentiation by first principles
lim [ f(x+h) - f(x) / h ]
Difference between f⁽²⁾ x and f² x
f⁽²⁾ x : 2nd derivative of x (dy/dx twice)
f²x : Power 2 to f(x)
When to use implicit differentiation?
When cannot make y the subject
2 main ideas of differentiation
- Differentiate both sides
- Can have both x and y in 1 term (use product / quotient rule)
2 main ideas of differentiation
- Differentiate both sides
- Can have both x and y in 1 term (use product / quotient rule)
Differentiation of inverse functions
sin⁻¹ x = 1 / √(1 - x²)
cos⁻¹ x = -1 / √(1 - x²)
tan⁻¹ x = 1 / (1 + x²)
Differentiation of e and ln/log
eˣ = eˣ
aˣ = aˣ ln a (**a must be a constant)
lnx = 1 / x
logₐx = 1 / (xlna)
Parametric differentiation
dy/dt = dy/dx x dx/dt
3 Important things for differentiation
- Simplify as much as possible first e.g. split ln
- See if can convert anything to simplify based on previous workings e.g. y OR dy/dx