Solved on Mar 24, 2024

Find the derivative of y=6xy=6x. Options: A. xx, B. 0, C. x2x^{2}, D. 66.

STEP 1

1. The expression y=6xy=6x represents a linear function of xx.
2. The notation yy^{\prime} represents the derivative of yy with respect to xx.
3. Basic rules of differentiation apply, such as the derivative of a constant times a variable is the constant.

STEP 2

1. Differentiate y=6xy=6x with respect to xx.
2. Identify the correct answer from the given options.

STEP 3

Differentiate the function y=6xy=6x with respect to xx using the power rule.
y=ddx(6x) y^{\prime} = \frac{d}{dx}(6x)

STEP 4

Apply the constant multiple rule, which states that the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function.
y=6ddx(x) y^{\prime} = 6 \frac{d}{dx}(x)

STEP 5

Use the fact that the derivative of xx with respect to xx is 1.
y=61 y^{\prime} = 6 \cdot 1

STEP 6

Simplify the expression to find the derivative.
y=6 y^{\prime} = 6

STEP 7

Compare the result with the given options.
The correct answer is D. 6.

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