Mathematics, 05.11.2020 20:10, u8p4

Differentiate the given function:

Answers: 2

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Answers

answered: saltedcaramel60

$\displaystyle h'(x) = \frac{1 + x - arcsin(x)\sqrt{1 - x^2}}{\sqrt{1 - x^2}(1 + x)^2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Algebra II

Simplifying

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

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

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Special Trig Derivatives:

Arcsine: $\displaystyle \frac{d}{dx}[arcsin(x)] = \frac{1}{\sqrt{1 - x^2}}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle h(x) = \frac{arcsin(x)}{1 + x}$

Step 2: Differentiate

Quotient Rule: $\displaystyle h'(x) = \frac{(1 + x)\frac{d}{dx}[arcsin(x)] - \frac{d}{dx}[1 + x][arcsin(x)]}{(1 + x)^2}$ Special Trig Derivative [Arcsine]: $\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - \frac{d}{dx}[1 + x][arcsin(x)]}{(1 + x)^2}$ Derivative Property [Addition/Subtraction]: $\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - (\frac{d}{dx}[1] + \frac{d}{dx}[x])[arcsin(x)]}{(1 + x)^2}$ Basic Power Rule: $\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - 1[arcsin(x)]}{(1 + x)^2}$ Multiply: $\displaystyle h'(x) = \frac{\frac{1 + x}{\sqrt{1 - x^2}} - arcsin(x)}{(1 + x)^2}$ Rewrite [Multiply]: $\displaystyle h'(x) = \frac{\frac{1 + x}{\sqrt{1 - x^2}} - arcsin(x)}{(1 + x)^2} \cdot \frac{\sqrt{1 - x^2}}{\sqrt{1 - x^2}}$ Simplify [Multiply]: $\displaystyle h'(x) = \frac{1 + x - arcsin(x)\sqrt{1 - x^2}}{\sqrt{1 - x^2}(1 + x)^2}$

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

Unit: Derivatives

Book: College Calculus 10e

answered: Guest

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation:

answered: Guest

The answer is d, none of above hope i

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