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

20 percentage, you can also do it on a calculator.

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.

Plz hurrywhat is the simplified form of  ? assume  x  ≠ 0.

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