Interpreting Derivative Notation

The video tutorial discusses a problem involving the function f(x) = cos(x) and its derivative. The main focus is on interpreting f'(3x) and the potential confusion arising from notation. The instructor explains two possible interpretations: taking the derivative first and then substituting 3x, or substituting 3x first and then taking the derivative. The latter approach involves using the chain rule, resulting in -sin(3x) multiplied by 3. The instructor advises against ambiguous notation and suggests a more natural interpretation. The video concludes with a discussion on the importance of clear mathematical notation.

What is the initial function given in the problem statement?

• f(x) = tan(x)

• f(x) = x^2

• f(x) = cos(x)

• f(x) = sin(x)

What is the derivative of f(x) = cos(x)?

• f'(x) = cos(x)

• f'(x) = sin(x)

• f'(x) = -sin(x)

• f'(x) = -cos(x)

What is the initial interpretation of f'(3x) according to the video?

• Negative sine of 3x

• Negative cosine of 3x

• Sine of 3x

• Cosine of 3x

What is the main issue with the notation f'(3x) as discussed in the video?

• It is too simple to be useful

• It is not a valid mathematical expression

• It can be interpreted in multiple ways

• It is too complex to solve

What are the two possible interpretations of f'(3x)?

• Subtract 3x first, then derivative or derivative first, then subtract 3x

• Derivative first, then plug in 3x or plug in 3x first, then derivative

• Multiply by 3x first, then derivative or derivative first, then multiply by 3x

• Add 3x first, then derivative or derivative first, then add 3x

What rule is suggested to correctly interpret f'(3x)?

• Chain rule

• Power rule

• Product rule

• Quotient rule

What advice is given regarding the notation f'(3x)?

• Use it only in simple problems

• Avoid using it due to ambiguity

• Always use it as it is

• It is the best notation to use