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katrin [286]
4 years ago
13

Which property is shown by -3 x (6+5) = -3 x 6+ -3 x 5

Mathematics
1 answer:
aniked [119]4 years ago
4 0

Answer:

The distributive property of multiplication

Step-by-step explanation:

we know that

The <u>distributive property of multiplication</u>  states that the product of a number by a sum, is equal to multiply each addend by the number (This is called distributing the number) and then, you can add the products

so

a*(b+c)=a*b+a*c

in this problem we have

-3*(6+5)=-3*6+-3*5 ----> the number -3 is distributed

therefore

We have the distributive property of multiplication

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Answer:

\displaystyle y' = \frac{-2}{x \ln (10)[\log (x) - 2]^2}

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

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

Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(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:

<u>Step 1: Define</u>

<em>Identify.</em>

\displaystyle y = \frac{\log (x)}{\log (x) - 2}

<u>Step 2: Differentiate</u>

  1. [Function] Derivative Rule [Quotient Rule]:                                                 \displaystyle y' = \frac{[\log (x) - 2][\log (x)]' - [\log (x) - 2]'[\log (x)]}{[\log (x) - 2]^2}
  2. Rewrite [Derivative Rule - Addition/Subtraction]:                                       \displaystyle y' = \frac{[\log (x) - 2][\log (x)]' - [\log (x)' - 2'][\log (x)]}{[\log (x) - 2]^2}
  3. Logarithmic Differentiation:                                                                         \displaystyle y' = \frac{[\log (x) - 2]\frac{1}{\ln (10)x} - [\frac{1}{\ln (10)x} - 2'][\log (x)]}{[\log (x) - 2]^2}
  4. Derivative Rule [Basic Power Rule]:                                                             \displaystyle y' = \frac{[\log (x) - 2]\frac{1}{\ln (10)x} - \frac{1}{\ln (10)x}[\log (x)]}{[\log (x) - 2]^2}
  5. Simplify:                                                                                                         \displaystyle y' = \frac{\frac{\log (x) - 2}{\ln (10)x} - \frac{\log (x)}{\ln (10)x}}{[\log (x) - 2]^2}
  6. Simplify:                                                                                                         \displaystyle y' = \frac{\frac{-2}{\ln (10)x}}{[\log (x) - 2]^2}
  7. Rewrite:                                                                                                         \displaystyle y' = \frac{-2}{x \ln (10)[\log (x) - 2]^2}

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

Unit: Differentiation

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