MATHEMATICS HIGH SCHOOL

Derivative of R=(100+50/lnx)

Answers

Answer 1

Answer:

Answer:

$\displaystyle R' = (-50)/(x(\ln x)^2)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle (d)/(dx) [(f(x))/(g(x)) ]=(g(x)f'(x)-g'(x)f(x))/(g^2(x))$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle R = 100 + (50)/(\ln x)$

Step 2: Differentiate

Derivative Property [Addition/Subtraction]: $\displaystyle R' = (d)/(dx)[100] + (d)/(dx) \bigg[ (50)/(\ln x) \bigg]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle R' = (d)/(dx)[100] + 50 (d)/(dx) \bigg[ (1)/(\ln x) \bigg]$
Basic Power Rule: $\displaystyle R' = 50 (d)/(dx) \bigg[ (1)/(\ln x) \bigg]$
Derivative Rule [Quotient Rule]: $\displaystyle R' = 50 \bigg(((1)' \ln x - (\ln x)')/((\ln x)^2) \bigg)$
Basic Power Rule: $\displaystyle R' = 50 \bigg( (-(\ln x)')/((\ln x)^2) \bigg)$
Logarithmic Differentiation: $\displaystyle R' = 50 \bigg( ((-1)/(x))/((\ln x)^2) \bigg)$
Simplify: $\displaystyle R' = (-50)/(x(\ln x)^2)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Related Questions

(2.3 x 10 to the power of 4) times ( 1.5x10 to the power of minus 3) in standard form
Anthony, who is 2 meters tall, is standing on top of a skyscraper that is 1 km tall. How many meters is it from the top of Anthony's head to the bottom of the skyscraper?
Solve the following equations. 1 − log8(x − 3) = log8(2x)
One side of a regular octagon is 4 inches long. What is the length of another side of the octagon?32 inches8 inches4 inchescan't be determined
Explain the distance formula. Then use it to calculate the distance between A(1,1) and B(7,-7).

Write the equation in standard form. 0.5x = y - 4

Answers

Answer:

y=0.5x+4

Step-by-step explanation:

0.5x= y-4

add 4 on both sides

and then you get:

y=0.5x+4

Answer:

y = 0.5x + 4, or y = 1/2x + 4 (if you prefer fractions)

Step-by-step explanation:

y = mx + b (slope intercept form / standard form) ; m = 0.5 or 1/2, b = 4.

m = linear coefficient/slope(denoted by a in a 1 degree binomial)

b = constant coefficient / y-intercept (denoted by b in a 1 degree binomial)

to convert this equation into a standard form equation. You need to isolate y and leave the coefficients on the other side.

0.5x = y - 4

0.5x (+4) = y - 4 (+4)

0.5x + 4 = y

y = 0.5x + 4

What 3 numbers multiply to get 63?

Answers

The three numbers to multiply to get 63 is A = 3 x 3 x 7

Given data ,

Let the number be represented as A

where the value of A = 63

Let the three numbers be represented as a , b , c

where the a , b , c are the factors of A

The factorization of the number 63 will be the three numbers to multiply to get the number 63

So , prime factorization of 63 is: 3 x 3 x 7

Hence , the three numbers are 3 , 3 and 7

To learn more about factorization click :

brainly.com/question/804076

#SPJ2

There are many combinations if the numbers are not required to be integers.

If they are required to be integers, I'd suggest:

3*7*3 = 63

How to cut 22 inches x 28 inches into 8 1/2 x 11
PLEASE HELP ME 20 POINTS!!!!!

Answers