Question

Find the derivatives of the given functions. Assume that $a, b, c,$ and $k$ are constants. $$g(t)=\frac{1}{t^{5}}$$

Name: Problem 17, Chapter 3: Calculus Single Variable
Uploaded: 2021-04-15T15:30:29-08:00
Duration: 1 min 20 s
Channel: Gregory Higby
Description: Find the derivatives of the given functions. Assume that a, b, c, and k are constants. g(t)=(1)/(t^5)

   Find the derivatives of the given functions. Assume that $a, b, c,$ and $k$ are constants.
$$g(t)=\frac{1}{t^{5}}$$

Calculus Single Variable

Deborah… 7th Edition

Chapter 3, Problem 17

Instant Answer

Solved by Expert Gregory Higby

04/15/2021

Step 1

We use the rule that $t^{-n}$ is the same as $\frac{1}{t^n}$. So, we can rewrite $g(t)$ as $t^{-5}$. Show more…

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Find the derivatives of the given functions. Assume that $a, b, c,$ and $k$ are constants. $$g(t)=\frac{1}{t^{5}}$$

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Key Concepts

Rewriting Functions Using Negative Exponents

Rewriting functions with reciprocals as functions with negative exponents, such as expressing 1/t^5 as t^(-5), is crucial because it allows the direct application of the power rule to compute the derivative efficiently. This is a common technique in simplifying differentiation of rational functions.

Power Rule

The power rule is a fundamental concept in calculus that states if a function is given by t^n, where n is any real number, its derivative is n multiplied by t raised to the power of (n-1). This rule simplifies the differentiation process for functions that involve powers of the variable.

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