Write this expression in simplified terms. 3×√3×6×√6

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

suppose that y varies inversely with x, and y=3 when x=5. what is an equation for the inverse variation

Angelina_Jolie [31]

The inverse variation of y=3 would be y=1/3
The inverse variation of x=5 would be x=1/5

You just need to flip the variation around.

Your answer is: y=1/3; x=1/5

Have an amazing day and stay hopeful!

7 0

3 years ago

An initial population of 415

slamgirl [31]

Answer:

The exponential function to model the duck population is:

f(n)=415*(1.32)^n, where:

x is the duck population

n is the number of years

Step-by-step explanation:

In order to calculate the duck population you can use the formula to calculate future value:

FV=PV*(1+r)^n

FV=future value

PV=present value

r=rate

n=number of periods of time

In this case, the present value is the initial population of 415 and the rate is 32%. You can replace these values on the formula and the exponential function to model the duck population would be:

f(n)=415*(1+0.32)^n

f(n)=415*(1.32)^n, where:

x is the duck population

n is the number of years

3 0

3 years ago

I can’t figure out which formula goes with which sequence. Help……. Please???

Radda [10]

For a geometric sequence

a, ar, ar ², ar ³, …

the n-th term in the sequence is ar ⁿ ⁻ ¹.

The first sequence is

1, 3, 9, 27, …

so it's clear that a = 1 and r = 3, and so the n-th term is 3ⁿ ⁻ ¹.

The second sequence is

400, 200, 100, 50, …

so of course a = 400, and you can easily solve for r :

200 = 400r ==> r = 200/400 = 1/2

Then the n-th term is 400 (1/2)ⁿ ⁻ ¹.

Similarly, the other sequences are given by

3rd: … 4 × 2ⁿ ⁻ ¹

4th: … 400 (1/4)ⁿ ⁻ ¹

5th: … 5ⁿ ⁻ ¹

6th: … 1000 (1/2)ⁿ ⁻ ¹

7th: … 2 × 5ⁿ ⁻ ¹

7 0

3 years ago

How do you solve 19=v-(-9)

leva [86]

V=10. You can solve this by using the rule of subtracting negative numbers, which means if you are subtracting a negative it is the same as adding a positive. So basically V + 9 = 19, making V equal 10.

5 0

3 years ago