Mathematics, 09.09.2020 06:01 pedrojsq271

Derivative of R=(100+50/lnx)

Answers: 1

Show answers

Answers

Answer from: wirchakethan23

$\displaystyle R' = \frac{-50}{x(\ln x)^2}$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

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

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

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle R = 100 + \frac{50}{\ln x}$

Step 2: Differentiate

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

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

Unit: Differentiation

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

The correct answer is 7

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Will mark brainliest if you answer ! the taco shop sold 198 lunches friday. this number is 3 more than 3 times the number they sold monday. let n represent the number of lunches sold monday. which equation shows an equality between two different ways of expressing the number of lunches sold on friday? a. n – 3 = 198 b. 3n – 3 = 198 c. 3n + 3 = 198 d. n + 3 = 198

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

What properties allow transformation to be used as a problem solving tool

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

What is the prime factorization of 23 ?me with this question

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size.it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?

Answers: 1

Answer

You know the right answer?

Derivative of R=(100+50/lnx)...

Questions