Factor.

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

7 0

3 years ago

If r=4 units and x = 8 units then what is the volume of the cylinder shown above use 3.14 for TT and round your answer to the ne

BARSIC [14]

To answer this you will use the formula V = pi x radius ^2 x height. The substitution for this would be 3.14 x 4^2 x 8. The approximate answer is 401.92 cubic units. 3.14 is an approximation of pi.

Note: It does not say that x is the height, but this is the only piece of information missing without an obvious label, so I am using it as the height.

3 0

4 years ago

Giles is searching for a sock and he discovers he has 10 socks for every 5 pair of shoes.If he has 20 socks, how many pairs of s

lutik1710 [3]

Answer:

10

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

According to Money magazine, Maryland had the highest median annual household income of any state in at (Time website). Assume t

Ad libitum [116K]

Answer:

The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of $Z = \frac{X - \mu}{\sigma}$ , in which $\mu$ is the mean income and $\sigma$ is the standard deviation of incomes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean $\mu$ , standard deviation $\sigma$

What is the probability that a household in Maryland has an annual income of X or more?

The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of $Z = \frac{X - \mu}{\sigma}$ , in which $\mu$ is the mean income and $\sigma$ is the standard deviation of incomes.

6 0

3 years ago

Simplify your answer as much as possible. :)

Nitella [24]

Answer:

y > 7

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers