The power rule is a commonly used rule in derivatives. The power rule basically states that the derivative of a variable raised to a power n is n times the variable raised to power n-1. The mathematical formula of power rule can be written as:
Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function’s derivatives.
Find the derivative of
Power Rule (with rewriting the expression)
From the above equation and example, you now know how to differentiate a variable raised to a power n. The point to be noted is that n can also be fractional and so the variable could have exponents and these exponents are real numbers. For better understanding check the following examples:
Find the derivate of
Justifying the Power Rule
Using the definition of derivative we can write
By using binomial theorem we expand (x + △x)n th term
Only the first term remained as it does not contain a △ x term hence,
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.