To differentiate the expression 5x with respect to x, we apply the basic rules of differentiation. The coefficient of x, which is 5 in this case, remains constant while we differentiate.
According to the power rule of differentiation, the derivative of x^n where n is a constant is n * x^(n-1). Here, we have ‘x’ which is equivalent to x^1. So, we can apply the power rule as follows:
1. Identify the coefficient which is 5.
2. Using the power rule: the derivative of x^1 is 1 * x^(1-1) = 1 * x^0 = 1.
3. Therefore, the derivative of 5x is simply 5 * 1 = 5.
In conclusion, the derivative of 5x is 5.