Power Rule
d/dx(1/x) = -1/(x^2)
The power rule is an important rule in calculus used to differentiate power functions. The power rule states that if f(x) = x^n, where n is a constant, then its derivative is given by:
f'(x) = nx^(n-1)
This means that if we want to find the derivative of any power function, we simply take the exponent, multiply it by the coefficient, and then reduce the exponent by 1.
For example, let’s say we want to find the derivative of f(x) = x^3. Using the power rule, we know that f'(x) = 3x^(3-1) = 3x^2. So, the derivative of x^3 is 3x^2.
The power rule is very useful for finding derivatives of polynomials and other functions that involve powers. It can simplify the process of finding derivatives and can save a lot of time and effort.
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