Mastering The Power Rule Of Differentiation: Derivative Of X^N With Respect To X Explained

d/dx (x^n)

nx^n-1

The derivative of x^n with respect to x is n*x^(n-1).

Proof:
Let y = x^n, where n is a constant. Then, taking the derivative with respect to x:

dy/dx = d/dx(x^n)

Using the power rule of differentiation, we can write:

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

Therefore, the derivative of x^n with respect to x is n*x^(n-1).

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