Other Power Rules in Calculus

There are various other power rules used in calculus that are used to solve various problems. Some of the various power rules in calculus are,

• Power Rule Integration
• Power Rule Exponents
• Power Rule Logarithms

Now let’s learn about these power rules in detail.

Power Rule Integration

Power rule in integration is helpful for finding the integral of expressions that are given as, xⁿ, where n is a real number and n ≠ -1. The formula for the integration power rule is,

∫xⁿ dx = xⁿ⁺¹/(n + 1) + C

where n ≠ -1. We can understand this rule using the example discussed below,

(i) ∫10x⁹ dx 

= 10(x⁹⁺¹)/(9+1) + C 

= 10x¹⁰/10 + C 

= x¹⁰ + C

(ii) ∫x^-3 dx

= x^-3+1/(-3+1) + C 

= -x^-2/2+ C 

= -1/2x² + C

Power Rule Exponents

Power rule in exponents is used we have to find the power of the exponents that are given as,

(x^m)ⁿ = x^mn

We can understand this rule using the example discussed below,

• (x²)⁴ = x^2×4 = x⁸
• (2^-3)^-3 = 2^-3×-3 = 2⁹

Power Rule Logarithms

The power rule in the logarithmic is used to solve the power of any logarithmic function such as,

log_n(a)^b = b.log_n(a)

We can understand this rule using the example discussed below,

• log₈x³ = 3log₈x

Read More,

• Applications of Power Rule
• Laws of Exponents

Power Rule is a fundamental rule in the calculation of derivatives that helps us find the derivatives of functions with exponents. Exponents can take any form, including any function itself. With the help of the Power Rule, we can differentiate polynomial functions, functions with variable exponents, and many more.

It is a very diverse tool in the arsenal of students who want to learn the process of differentiation. This article covers the Power Rule, including its formula and derivation, solved examples, applications in calculus, and various commonly asked curious questions related to the Power Rule.