derivative power rule
The power rule is a fundamental rule in calculus that helps us find the derivative of a function that is in the form of a power
The power rule is a fundamental rule in calculus that helps us find the derivative of a function that is in the form of a power. The power rule states that if you have a function of the form f(x) = x^n, where n is a constant, then the derivative of that function f'(x) is given by f'(x) = n*x^(n-1).
Let’s go through an example to see how the power rule works.
Example: Find the derivative of the function f(x) = 3x^2.
Solution: According to the power rule, we can differentiate each term of the function separately.
Taking the derivative of the first term, 3x^2, we use the power rule:
d/dx (3x^2) = 2 * 3x^(2-1) = 6x^1 = 6x.
So, the derivative of the first term is 6x.
Since f(x) only has one term, the derivative of the whole function f(x) = 3x^2 is simply 6x.
In general, if we have a function f(x) = ax^n, where a is a constant and n is a constant exponent, the derivative will be f'(x) = anx^(n-1).
It is important to note that the power rule only applies when we have a single term raised to a constant power. If we have multiple terms, we need to use other rules like the sum rule or product rule to find the derivative.
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