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3 years ago

Find the derivative of f(x)=x+1/x-1 using first principal

Mathematics

1 answer:

zepelin [54]3 years ago

5 0

f ' ( x ) = 1 ( x + 1 ) 2

Explanation:

differentiating from first principles

f ' ( x ) = lim h → 0

f ( x + h ) − f ( x ) h

f ' ( x ) = lim h → 0

x + h x + h + 1 − x x + 1 h

the aim now is to eliminate h from the denominator

f ' ( x ) = lim h =0

( x + h ) ( x + 1 )− x ( x + h + 1) h ( x + 1 ) ( x + h + 1 )

f ' ( x ) = lim h → 0

x 2 + h x + x + h − x 2 − h x − x h ( x + 1 ) ( x+h + 1 )

f ' ( x ) = lim h → 0

h 1 h 1 ( x + 1 ) ( x + h +1 )

f ' ( x ) = 1 ( x + 1 ) 2

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Please help me with the problem

Kruka [31]

Oh my gosh...thats a lot. Umm, well let's start with what the equation says. This will break it down to where it's of better understanding. What is the equation asking you to do? You have heard of the acronym "PEMDAS", correct? (Parantheses, Exponents, Multiplication, Division, Addition and Subtraction) Follow that order of operations and see what it is the equation wants done first. Solve it, basically...then we will focus on the actual question parts.

6 0

3 years ago

Read 2 more answers

A soccer player uses her head to hit a ball up in the air from a height of 2 meters with an initial vertical velocity of 5 meter

ozzi

Answer:

The ball will hit the ground in 1.33 s if no one touches it. The equation has 2 real solutions.

Step-by-step explanation:

The ball will hit the ground when its height is equal to 0 meters, therefore using this value in the expression and solving for "t" will give us the correct solutions.

$h = -4.9*t^2 + 5*t + 2\\\\-4.9*t^2 + 5*t + 2 = 0\\\\t_{1,2} = \frac{-5 \pm \sqrt{5^2 - 4*(-4.9)*(2)}}{2*(-4.9)}\\\\t_{1,2} = \frac{-5 \pm \sqrt{64.2}}{-9.8}\\\\t_{1,2} =\frac{-5 \pm 8.0125}{-9.8}\\\\t_1 = \frac{-5 - 8.0125}{-9.8} = 1.33 \text{ s}\\\\t_2 = \frac{-5 + 8.0125}{-9.8} = -0.3 \text{ s}$

The ball will hit the ground in 1.33 s if no one touches it. The equation has 2 real solutions.

8 0

3 years ago

Write the equation of the line that passes through the points (3,-8) and (-8,1).

Gennadij [26K]

Answer:

-9/11

Step-by-step explanation:

-8-1/3-(-8)

-9/11

6 0

3 years ago

I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST! A circle has a diameter AB, and its center is at (-3, 3). Point A is at (1/2,6)

kow [346]

Using the mid-point concept, it is found that point B is located at coordinates (-6.5, 0).

<h3>What is the midpoint concept?</h3>

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

The center is the midpoint of the two coordinates of the diameter, hence:

$C = \frac{B + A}{2}$

For the x-coordinate:

$-3 = \frac{x + 0.5}{2}$

x + 0.5 = -6

x = -6.5

For the y-coordinate:

$3 = \frac{y + 6}{2}$

y + 6 = 6

y = 0

More can be learned about the mid-point concept at brainly.com/question/10956693

#SPJ1

3 0

2 years ago

HELP QUICK !’ ***What is the area of a circle with a diameter of 126 in?

Vladimir79 [104]

Answer:

49,850.64

Step-by-step explanation:

To find the area of a circle, you must use the formula pi r ^2 (pi r squared).

In this case, we are using 3.14 for pi, so we can add that into the formula.

3.1r^2

We also know the radius, so we can add that in too.

3.14 x 126 ^2

Now solve.

126^2 = 15,876

15,876 x 3.14 = 49,850.64

49,850.64 is the answer.

Hope this helped!

8 0

3 years ago

Find the derivative of f(x)=x+1/x-1 using first principal​

Find the derivative of f(x)=x+1/x-1 using first principal