d/dx [x^n]
To find the derivative of a function with respect to x, we can use the power rule of differentiation
To find the derivative of a function with respect to x, 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, where n is a constant, then the derivative is given by:
d/dx [x^n] = n * x^(n-1)
Let’s apply this rule to find the derivative of the function f(x) = x^n:
d/dx [x^n] = n * x^(n-1)
So, the derivative of x^n with respect to x is n * x^(n-1).
For example, let’s find the derivative of the function f(x) = x^3:
d/dx [x^3] = 3 * x^(3-1)
= 3 * x^2
Therefore, the derivative of x^3 with respect to x is 3x^2.
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