The formula for finding the derivative of 1/x^n is d/dx(1/x^n) = -n/x^(n+1)
The derivative of 1/x^n is equal to -n/x^(n+1) because it follows the power rule for derivatives, which states that the derivative of x^n is equal to nx^(n-1). In this case, n is a constant, so it remains unchanged while x^n becomes x^(n-1), resulting in -n/x^(n+1).
Yes, the derivative of 1/x^n can be simplified further by factoring out a negative sign, resulting in n/x^(n+1).
The derivative of 1/x^n is significant because it allows us to find the instantaneous rate of change of a function, which is useful in many real-world applications such as physics, economics, and engineering.
The derivative of 1/x^n can be applied in real life to calculate the slope of a curve at a specific point, find the maximum or minimum values of a function, and analyze the behavior of a function over time. It is also used in optimization problems to find the most efficient solution.