Please answer the question that is in the photo attached below

Mathematics

1 answer:

lesantik [10]3 years ago

4 0

Square root of 28

explanation:

a^2 + b^2 = c^2

a^2+6^2 = 8^2

a^2+36=64

subtract 36 from both sides

a^2=28

square root both sides

a = square root of 28

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Answer:

$y'= \frac{3x+2}{2\sqrt{x} }$

General Formulas and Concepts:

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$y=\sqrt{x} (x+2)$

Step 2: Rewrite

$y=x^{\frac{1}{2} } (x+2)$

Step 3: Differentiate

Product Rule [Basic Power/Chain Rule]: $y'= \frac{1}{2} x^{\frac{1}{2} -1}(x+2)+x^{\frac{1}{2} }(1)$
Simplify: $y'= \frac{1}{2} x^{\frac{-1}{2}}(x+2)+x^{\frac{1}{2}}$
Rewrite: $y'= \frac{x+2}{2\sqrt{x} } + \sqrt{x}$
Add: $y'= \frac{3x+2}{2\sqrt{x} }$