Question

What is the derivative of 66lnx +135
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Answer 1

`\displaystyle (dy)/(dx) = (66)/(x)`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:
`\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)`

Derivative Property [Addition/Subtraction]:
`\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]`

Explanation:

Step 1: Define

Identify

`\displaystyle y = 66 \ln x + 135`

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:
   `\displaystyle y' = (d)/(dx)[66 \ln x] + (d)/(dx)[135]`
2. Derivative Property [Multiplied Constant]:
   `\displaystyle y' = 66(d)/(dx)[\ln x] + (d)/(dx)[135]`
3. Logarithmic Differentiation:
   `\displaystyle y' = (66)/(x)`

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

Unit: Differentiation