Answer:

General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
- Terms/Coefficients
- Functions
- Function Notation
Algebra II
Calculus
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Property [Addition/Subtraction]:
![\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]](https://img.qammunity.org/2021/formulas/mathematics/college/kqosumt4896r7x44jgtw0o7kk6g4d3irvr.png)
Derivative Rule [Quotient Rule]:
![\displaystyle (d)/(dx) [(f(x))/(g(x)) ]=(g(x)f'(x)-g'(x)f(x))/(g^2(x))](https://img.qammunity.org/2021/formulas/mathematics/college/526v84fft3iovys57h8fyaznapbe78t2md.png)
Special Trig Derivatives:
- Arcsine:
![\displaystyle (d)/(dx)[arcsin(x)] = (1)/(√(1 - x^2))](https://img.qammunity.org/2021/formulas/mathematics/college/72n6zh7ktekuzcdkyizb0607d1hi7t92dx.png)
Explanation:
Step 1: Define
Identify

Step 2: Differentiate
- Quotient Rule:
![\displaystyle h'(x) = ((1 + x)(d)/(dx)[arcsin(x)] - (d)/(dx)[1 + x][arcsin(x)])/((1 + x)^2)](https://img.qammunity.org/2021/formulas/mathematics/college/9onbcu162vpq0l8jayfd1gj0xxlnixl4vd.png)
- Special Trig Derivative [Arcsine]:
![\displaystyle h'(x) = ((1 + x)((1)/(√(1 - x^2))) - (d)/(dx)[1 + x][arcsin(x)])/((1 + x)^2)](https://img.qammunity.org/2021/formulas/mathematics/college/7f63yzkp0t0y8mjatl26l4mtf9katxylrc.png)
- Derivative Property [Addition/Subtraction]:
![\displaystyle h'(x) = ((1 + x)((1)/(√(1 - x^2))) - ((d)/(dx)[1] + (d)/(dx)[x])[arcsin(x)])/((1 + x)^2)](https://img.qammunity.org/2021/formulas/mathematics/college/gq1fyyswi7c6zowuxgm0tnralde32b5gwh.png)
- Basic Power Rule:
![\displaystyle h'(x) = ((1 + x)((1)/(√(1 - x^2))) - 1[arcsin(x)])/((1 + x)^2)](https://img.qammunity.org/2021/formulas/mathematics/college/eq3f6sp53o8n16uengais3j7hgd3myl9lq.png)
- Multiply:

- Rewrite [Multiply]:

- Simplify [Multiply]:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e