C12-16 Flashcards
1
Q
differentiating a constant
A
equals 0
2
Q
differentiating a linear
A
equals a constant
3
Q
differentiating a square
A
equals a linear
4
Q
differentiating sin(x)
A
equals cos(x)
5
Q
if f and g are differentiable at a then ?
A
then f+g is differentiable at a and
f+g)’(a) = f’(a) + g’(a
6
Q
what is the product rule?
A
f’ g + f g’
7
Q
if f(x) = x^n for nEN then
A
f’(x) = na^(n-1)
8
Q
what is the quotient rule?
A
(f’ g - f g’)/ g^2
9
Q
f= sin(x)
A
f’ = cos(x)
10
Q
f
cos(x)
A
f’
-sin(x)
11
Q
f
tan(x)
A
f’
sec^2(x)
12
Q
f
sec(x)
A
f’
sec(x) tan(x)
13
Q
f
cosec(x)
A
f’
-csc(x) cot(x)
14
Q
f
cot(x)
A
f’
-csc^2(x)
15
Q
considering function f on an interval I on which it is differentiable and invertible on I by f^(-1)
A
for all bE I where f’(b) does not equal 0, the inverse function f^(-1) is then differentiable at a= f(b) and
(f^-1)’ (a) = 1/(f’(b)) = 1/ (f’(f^-1(a))
