Understanding the Power Rule in Calculus | Differentiating Functions with Constant Exponents

Power Rule

The power rule is a fundamental rule in calculus that allows us to differentiate functions of the form y = x^n, where n is a constant exponent

The power rule is a fundamental rule in calculus that allows us to differentiate functions of the form y = x^n, where n is a constant exponent.

According to the power rule, if we have a function y = x^n, then its derivative is given by:

dy/dx = nx^(n-1)

In simpler terms, when we differentiate a function y = x^n, we multiply the exponent n by the coefficient in front of x and decrease the exponent by 1.

For example, let’s consider the function y = 3x^2. To find its derivative, we can apply the power rule:

dy/dx = 2 * 3x^(2-1)
= 6x

So, the derivative of y = 3x^2 is 6x. This means that for any value of x, the slope of the tangent line to the curve y = 3x^2 is 6x.

The power rule is a powerful tool in calculus as it allows us to easily differentiate polynomial functions and expressions involving powers. It simplifies the process of finding derivatives and is used extensively in applications of calculus such as optimization and rate of change problems.

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