Question

Find the derivative. $F(t)=t^{2}+\frac{1}{t^{2}}$

   Find the derivative. 
$F(t)=t^{2}+\frac{1}{t^{2}}$

Calculus

Earl W. Swokowski 5th Edition

Chapter 3, Problem 27

Instant Answer

Solved by Expert Nick Johnson

03/16/2022

Step 1

Step 1: Rewrite the function $F(t)=t^{2}+\frac{1}{t^{2}}$ as $F(t)=t^{2}+t^{-2}$ to make it easier to differentiate. Show more…

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Find the derivative. $F(t)=t^{2}+\frac{1}{t^{2}}$

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Key Concepts

Differentiation

Differentiation is the process of finding the derivative of a function, which represents the rate at which the function's value changes with respect to changes in its input variable. It is a fundamental concept in calculus used to analyze the behavior and rates of change in functions.

Power Rule

The power rule is a basic rule of differentiation that allows for the easy calculation of the derivative of a function of the form f(t) = t^n, where n is any real number. It states that the derivative is n*t^(n-1), which simplifies the process of finding derivatives of polynomial and power functions.

Sum Rule

The sum rule in differentiation allows us to differentiate a function that is composed of the sum of two or more functions by differentiating each term separately. This rule simplifies the process by breaking down complex functions into simpler parts, each of which can be handled individually.

Negative Exponents

Negative exponents represent reciprocal functions, where t^(-n) is equivalent to 1/t^n. When differentiating functions with negative exponents, the power rule is applied in the same manner by treating the negative exponent as any other constant, which then influences the sign and power of the derivative accordingly.

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