d/dx [x^n]
nx^n-1 (power rule)
To find the derivative of x raised to the power of n, where n is a constant, we can use the power rule of differentiation.
According to the power rule, if we have a function f(x) = x^n, then its derivative f'(x) can be obtained by multiplying the exponent n with the coefficient of x, which is 1. Then, we subtract 1 from the exponent to get the new exponent.
Therefore,
d/dx [x^n] = n(x^(n-1))
For example, if we have x^3, its derivative is:
d/dx [x^3] = 3(x^(3-1)) = 3x^2
Similarly, if we have x^5, its derivative is:
d/dx [x^5] = 5(x^(5-1)) = 5x^4
And so on.
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