step 1 In this question, we want to find a differential. So let's take the steps. We're going to do the

Question

$d\left(8^{x}+x^{8}\right)$

Name: Problem 30, Chapter 4: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2019-06-14T13:15:58-08:00
Duration: 38 s
Channel: Bahar Tehranipoor
Description: d(8^x+x^8)

   $d\left(8^{x}+x^{8}\right)$

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 3rd Edition

Chapter 4, Problem 30

Instant Answer

Solved by Expert Bahar Tehranipoor

06/14/2019

Step 1

This function is a sum of two terms, so we can differentiate each term separately. Show more…

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$d\left(8^{x}+x^{8}\right)$

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Key Concepts

Sum Rule

The sum rule in differentiation states that the derivative of a sum of functions is the sum of their individual derivatives. This means you can differentiate each term separately and then add the results together.

Exponential Function Differentiation

When differentiating an exponential function of the form a raised to the power x, the derivative is given by a^(x) multiplied by the natural logarithm of the base a. This rule is essential for handling exponential expressions where the base is a constant and the exponent is a variable.

Power Rule

The power rule is used to differentiate functions of the form x raised to a constant exponent. It states that the derivative is the exponent multiplied by x raised to the power of one less than the original exponent. This rule is fundamental for dealing with polynomial expressions.

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