Core 3 Flashcards
How do you differentiate (ax+b) to the power of n?
an*(ax+b) to the power of (n-1)
How do you integrate d*(ax+b) to the power of n? (with respect to x)
(d over a(n+1))(ax+b) to the power of (n+1), then add a constant
What is true of the common ratio of an exponential growth function? What about a decay function?
Growth: r > 1
Decay: 1 > r > 0
What is the difference between discrete and continuous exponentials?
Discrete exponentials can only have set values for time, whereas continuous exponentials can have any time value.
If log base a of b = c, what does b equal?
b=a^c
What is the standard form of an exponential function?
A(value after time t)=a(original value)*e^(kt)
How do you differentiate ln(ax+b)?
1/(ax+b)*differential of (ax+b)
Explain the chain rule
The bracket is given the name u, and the function is differentiated in terms of u. u is then differentiated individually, and both results are multiplied to give the answer, with the value of u being replaced in at the end
What is the formula for differentiating 2 brackets (u and v) which are being multiplied together and what is this called?
u’v+uv’ (the ‘ denotes a derivative)
This is the Product Rule
What is the formula for differentiating 2 brackets (u and v) where one is being divided by the other and what is this called?
(u’v+uv’) divided by v^2 (the ‘ denotes a derivative)
This is the Quotient Rule
A function must have each input produce exactly one output. What can be done if this is not the case?
Restrict the domain
If you know the range of a function, what do you, therefore, know about its inverse?
The domain
When performing composite functions, which is performed first?
The one closest to the x
What is the restriction on inverses of functions?
They only exist for one-to-one functions
Due to the restriction of the domain of sin, what is true of arcsin?
It is entirely above the x axis
