Step-by-step explanation:
Derivation using Product rule : -
To find the derivative of f(x) = sin 2x by the product rule, we have to express sin 2x as the product of two functions. Using the double angle formula of sin, sin 2x = 2 sin x cos x. Let us assume that u = 2 sin x and v = cos x. Then u' = 2 cos x and v' = -sin x. By product rule,
f '(x) = uv' + vu'
= (2 sin x) (- sin x) + (cos x) (2 cos x)
= 2 (cos2x - sin2x)
= 2 cos 2x
This is because, by the double angle formula of cos, cos 2x = cos2x - sin2x.
Thus, derivation of sin 2x has been found by using the product rule.
Answer:
231
Step-by-step explanation:
A perfect fifth above a note has a frequency ratio of 3 to 2.
Therefore, we can set the proportion:
164.81 : x = 2 : 3
which gives:
x = <span>164.81 </span>× 3 ÷ 2
= 247.21
Hence, the perfect fifth above E₃ will have a frequency of 247.21Hz which corresponds to a B₃.
Answer:
x=2
Step-by-step explanation:
3 hours x 60min/hr = 180 minutes
45 x 4 = 180 minutes
15 x 4 = 60 sandwiches
