In probability, you study the chances, odds or likelihood of the event occurring. This is determined by dividing the number of possibilities to the total number of events. But terms may come up such as 'mutually exclusive'. Suppose, event A is for students ages 5-10, while event B is for students ages 11-15. The events A and B are said to be mutually exclusive when they do not intersect or meet at some point. In other words, when a student is in group A, he cannot be in group B because that becomes invalid and untrue. That seems logical because a student cannot be both 6 years old and 12 years old, right?

Hence, the answer to this question is letter C.

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Differentiate Vx(x + 2) with respect to x.

Travka [436]

Answer:

$y'= \frac{3x+2}{2\sqrt{x} }$

General Formulas and Concepts:

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$y=\sqrt{x} (x+2)$

Step 2: Rewrite

$y=x^{\frac{1}{2} } (x+2)$

Step 3: Differentiate

Product Rule [Basic Power/Chain Rule]: $y'= \frac{1}{2} x^{\frac{1}{2} -1}(x+2)+x^{\frac{1}{2} }(1)$
Simplify: $y'= \frac{1}{2} x^{\frac{-1}{2}}(x+2)+x^{\frac{1}{2}}$
Rewrite: $y'= \frac{x+2}{2\sqrt{x} } + \sqrt{x}$
Add: $y'= \frac{3x+2}{2\sqrt{x} }$