Final answer:
None of the listed functions (1) x², (2) sin(x), (3) ln(x), (4) e˥ require the use of the chain rule to find their derivatives, as they can each be derived using basic differentiation rules.
Step-by-step explanation:
The question asks which of the following functions does not require the use of the chain rule to find its derivative: 1) Derivative of x² 2) Derivative of sin(x) 3) Derivative of ln(x) 4) Derivative of e˥. To clarify, the chain rule is a formula for computing the derivative of the composition of two or more functions. For example, if you have a function h(x) that can be expressed as the composition of f(g(x)), then the derivative of h with respect to x is the derivative of f with respect to g times the derivative of g with respect to x.
When we examine the functions listed:
- Derivative of x² does not require the chain rule because it is a basic power function, and its derivative can be found by simply using the power rule.
- Derivative of sin(x) does not require the chain rule as it is a simple trigonometric function, and its derivative is cos(x).
- Derivative of ln(x) does not require the chain rule because it is a basic logarithmic function, and its derivative is 1/x.
- Derivative of e˥ does not require the chain rule because it is an exponential function, and its derivative is itself, e˥.
Therefore, none of the functions listed require the use of the chain rule for their derivatives.