Equations for Pure Flashcards
sin²x+cos²x = ….
1
tanx =
sinx / cosx
How can you attain new identities through sin²x+cos²x ?
By dividing through by sin²x or cos²x to attain cosec and sec values
sec²x =
tan²x + 1
cosec²x =
1 + cot²x
What part of a curve goes from a negative to positive gradient and has a positive second derivative?
A convex curve
V shape
What is the second derivative of a concave curve?
The second derivative is NEGATIVE!!!!!
the gradient goes from pos to neg
What are the derivatives of a stationary point of inflection?
The first derivative is the same either side
The first derivative zero
The second derivative is zero
What are the derivatives of a non stationary point of inflection?
The first derivative is the same either side
The first derivative is NOT zero
The second derivative is zero
What are the derivatives of a Stationary point, Local minimum or maximum?
The first derivative is ZERO
The first derivative changes either side of the point
The second derivative is POS (minimum) NEG (maximum)
What is the chain rule ( how would you differentiate two functions multiplied together? )
y’ = y’du x u’dx
Where you separate the function into y = u and u = the function and differentiate from there
How can you differentiate a function that is in terms of x rather than y?
dx/dy = 1/ dy/dx
Therefore, differentiate and take the reciprocal in terms of x!!!!!!!!!!
What is the product rule?
If y = u x v
y’ = u’v + v’u
(or y’ = v’u + u’v)
What is the quotient rule?
if y = u / v
y’ = u’v - v’u / v²
Cos ( A + B ) =
CosACosB - SinASinB
