You can either use the inverse function theorem or compute the general derivative using implicit differentiation. The first method is slightly faster.
The IFT goes like this: if f(x) is invertible and f(a) = b, then finv(b) = a (where "finv" means "inverse of f").
By definition of inverse functions, we have
f(finv(x)) = finv(f(x)) = x
Differentiating both sides of the second equality with respect to x using the chain rule gives
finv'(f(x)) * f'(x) = 1
When x = a, we get
finv'(b) * f'(a) = 1
or
finv'(b) = 1/f'(a)
Now let f(x) = sin(x), which is invertible over the interval -π/2 ≤ x ≤ π/2. In the interval, we have sin(x) = √3/2 when x = π/3. We also have f'(x) = cos(x).
So we take a = π/3 and b = √3/2. Then
arcsin'(√3/2) = 1/cos(π/3) = 1/(1/2) = 2
Answer:
B) 4 one-point baskets: 5 three-point baskets
Step-by-step explanation:
(4 x 1) + (5 x 3) = 19
<h2>
Answer:</h2>
This statement is false.
Step-by-step explanation:
Credit cards can only lead to debt that is difficult to eliminate and should be avoided at all costs. This is false.
This is not a standard statement that credit cards always lead to debt. A person should use his credit card with responsibility. He should pay the bills timely to avoid accumulation of debt and other fines. Only when a person uses his card irresponsibly and does not pay dues timely, can lead to debts.
So, this is a false statements.
2/3 of a box per 30 secs
2/3 times 2 = 4/3 = 1 1/3
Answer:
15in
Step-by-step explanation:
Convert the 15 ft to inches (180) and then set up the proportion.\frac{1}{12} = \frac{x}{180}121=180x . Cross multiply to get that 12x = 180 and x = 15 inches.