Mathematics, 06.01.2021 16:20 mremoney530

$r = \frac{a { }^{2} + 2a - 7 }{ \sqrt{a} }$ differentiate this using the quotient rule

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Answer from: pearfam98

$\frac{dr}{da} = \frac{3a^2 + 2a + 7}{2a^{\frac{3}{2} }}$

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Expand by FOIL (First Outside Inside Last)Terms/Coefficients/Degrees

Algebra II

Exponential Rule: $x^{-m}= \frac{1}{x^m}$ Exponential Rule: $\sqrt{x} = x^{\frac{1}{2} }$

Calculus

Derivatives

Derivative Notation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

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

$r = \frac{a^2+2a-7}{\sqrt{a}}$

Step 2: Rewrite

$r = \frac{a^2+2a-7}{a^{\frac{1}{2} }}$

Step 3: Differentiate

Quotient Rule [Basic Power: $\frac{dr}{da} = \frac{a^{\frac{1}{2} }(2a^{2-1} + 2a^{1-1}) - \frac{1}{2}a^{\frac{1}{2} - 1 }(a^2 + 2a + 7)}{(a^{\frac{1}{2} })^2}$ Simplify: $\frac{dr}{da} = \frac{a^{\frac{1}{2} }(2a + 2) - \frac{1}{2}a^{-\frac{1}{2}}(a^2 + 2a + 7)}{a}$ Simplify: $\frac{dr}{da} = \frac{2}{2} \cdot \frac{a^{\frac{1}{2} }(2a + 2) - \frac{1}{2}a^{-\frac{1}{2}}(a^2 + 2a + 7)}{a}$ Multiply: $\frac{dr}{da} = \frac{2a^{\frac{1}{2} }(2a + 2) - a^{-\frac{1}{2}}(a^2 + 2a + 7)}{2a}$ Factor: $\frac{dr}{da} = \frac{a^{-\frac{1}{2}}[2a(2a + 2) - (a^2 + 2a + 7)]}{2a}$ [Brackets] Distribute: $\frac{dr}{da} = \frac{a^{-\frac{1}{2}}[4a^2 + 4a - a^2 - 2a - 7]}{2a}$ [Brackets] Combine Like Terms: $\frac{dr}{da} = \frac{a^{-\frac{1}{2}}[3a^2 + 2a - 7]}{2a}$ Simplify: $\frac{dr}{da} = \frac{3a^2 + 2a + 7}{2a^{\frac{3}{2} }}$

Answer from: Quest

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered

Answer from: Quest

what are you trying find out?

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