Question

Find the derivative of the function y = 567x.

Answer 1

The derivative of the function y = 567x is 567.

Step-by-step explanation:

To find the derivative of the given function y = 567x, we apply the power rule of differentiation. The power rule states that if f(x) = ax^n, where a and n are constants, then the derivative f'(x) is given by multiplying the exponent by the coefficient. In this case, the function y = 567x is a simple linear function where the coefficient of x is 567. Applying the power rule, the derivative is calculated as follows:

`\[ (d)/(dx)(567x) = 567 \]`

Therefore, the derivative of y = 567x is 567. This result signifies that the rate of change of the function with respect to x is a constant value of 567, indicating a straight-line relationship with a constant slope of 567. Understanding derivatives is fundamental in calculus and provides insights into the instantaneous rate of change of a function at any given point.