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Natalija [7]
3 years ago
9

Derivative of

%7D%20%7D%20" id="TexFormula1" title=" \frac{ {3x}^{2} - 2x - 1 }{ {x}^{2} } " alt=" \frac{ {3x}^{2} - 2x - 1 }{ {x}^{2} } " align="absmiddle" class="latex-formula">
Show a step.​
Mathematics
1 answer:
Anastaziya [24]3 years ago
5 0

Answer:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

Step-by-step explanation:

we would like to figure out the derivative of the following:

\displaystyle  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

to do so, let,

\displaystyle y =  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

By simplifying we acquire:

\displaystyle y =  3 -  \frac{2}{x}  -  \frac{1}{ {x}^{2} }

use law of exponent which yields:

\displaystyle y =  3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} }

take derivative in both sides:

\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  (3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} } )

use sum derivation rule which yields:

\rm\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  3 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

By constant derivation we acquire:

\rm\displaystyle  \frac{dy}{dx} =  0 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

use exponent rule of derivation which yields:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ - 1 -1} ) -     ( - 2 {x}^{  - 2 - 1} )

simplify exponent:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ -2} ) -     ( - 2 {x}^{  - 3} )

two negatives make positive so,

\displaystyle  \frac{dy}{dx} =   2 {x}^{ -2} +      2 {x}^{  - 3}

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

\displaystyle  \frac{dy}{dx} =   \frac{2 }{x^2}+       \frac{2}{x^3}

simplify addition:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

and we are done!

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17. (a) The formula with CP subject is CP=\frac{SP}{1.1}

(b) The Cost Price of item without GST is $59.50

(c) The GST of item is $5.95

Step-by-step explanation:

Given formula is;

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SP = Selling price

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(a) Rearrange the formula to make CP the subject;

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Dividing both sides by 1.1

\frac{SP}{1.1}=\frac{1.1*CP}{1.1}\\\\\frac{SP}{1.1}=CP\\\\CP=\frac{SP}{1.1}

The formula with CP subject is CP=\frac{SP}{1.1}

(b) Use your formula from (a) to find the Cost Price of an item without GST if the selling price is $65.45

SP = $65.45

CP=\frac{65.45}{1.1}\\\\CP=\$59.50

The Cost Price of item without GST is $59.50

(c) Calculate the amount of GST on an item whose selling price is $65.45.

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GST = $5.95

The GST of item is $5.95

Keywords: percentage, multiplication

Learn more about multiplication at:

  • brainly.com/question/10764770
  • brainly.com/question/1087090

#LearnwithBrainly

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