Derivative of y = cx^n
To find the derivative of y = cx^n, where c is a constant and n is a real number, we can use the power rule of differentiation. The power rule states that if y = cx^n, then the derivative dy/dx is given by:

dy/dx = n * cx^(n-1)
Let's break down the steps to find the derivative:
1. Apply the power rule:
- Start by applying the power rule, which states that the derivative of x^n is n*x^(n-1). In this case, the exponent n remains the same, and we bring it down to multiply with the coefficient c.
2. Derivative of cx^n:
- Using the power rule, the derivative of cx^n is n*cx^(n-1). This is the derivative of y with respect to x.
3. Final result:
- Therefore, the derivative of y = cx^n is dy/dx = n * cx^(n-1). This formula gives us the rate of change of y with respect to x when y is a power function of x.
By following these steps and applying the power rule of differentiation, we can easily find the derivative of y = cx^n. This concept is fundamental in calculus and is used to calculate rates of change in various scientific and mathematical applications.