D of x^n
nx^n-1
The derivative of a function x^n is given by:
d/dx(x^n) = nx^(n-1)
Here, n is a constant or an exponent. To obtain the derivative of x^n, we subtract 1 from the exponent and multiply the resulting term with the coefficient (n). Then the base (x) remains the same.
Let’s take an example to understand this formula more clearly:
Example:
Find the derivative of f(x) = x^4
Solution:
We can use the formula to find the derivative of the given function.
d/dx(x^4) = 4x^(4-1)
d/dx(x^4) = 4x^3
Therefore, the derivative of f(x) = x^4 is 4x^3.
Note that this formula applies to all power functions, regardless of the value of n.
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