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:
(E) 90°
Step-by-step explanation:
The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle.
Any angle of a rectangle is 90°.
_____
Adjacent angles of a parallelogram are supplementary. If the diagonals are the same length, the triangles formed by either diagonal are congruent with the triangles formed by the other diagonal. This means adjacent angles are congruent. Congruent supplementary angles are 90°.
Answer:4 : 3
Step-by-step explanation:
32:48
8 : 6
4 : 3
The value of the expression is 98x
Answer:
A
Step-by-step explanation:
86.50 times 20
24.50 times 20
1,730-490= 1,240
1,240 divvied by 0.25 = 310