Derivation of x^n | The Power Rule Explained with Examples

dy/dx x^n

The expression “dy/dx” represents the derivative of the dependent variable y with respect to the independent variable x

The expression “dy/dx” represents the derivative of the dependent variable y with respect to the independent variable x. In other words, it measures the rate at which the function y changes when x changes.

To find the derivative of x raised to the power of n (x^n), we can use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = x^n, then its derivative f'(x) is given by:

f'(x) = n * x^(n-1)

Using this rule, we can differentiate x^n with respect to x and obtain:

d/dx (x^n) = n * x^(n-1)

Therefore, the derivative of x raised to the power of n is n times x raised to the power of (n-1).

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