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find from first principle the derivative of 3x+5/√x
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find from first principle the derivative of 3x+5/√x
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Mathematics
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2021-07-24T02:09:10+00:00
2021-07-24T02:09:10+00:00 1 Answers
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Answer:
[tex]\displaystyle \frac{d}{dx} = \frac{3x – 5}{2x^\bigg{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Algebra I
Calculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]
Step 2: Differentiate
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e