Find the given derivative. √²-1) 6 Dx 4x 3 X I Dx 4x 1 6 + 413 =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Title: Calculating the Derivative of a Function**

**Objective:**

Find the derivative of the given mathematical expression.

**Expression:**

Given:
\[ D_x \left( 4x^{-\frac{1}{3}} + \frac{6}{x^{\frac{4}{3}}} \right) \]

**Task:**

Calculate the derivative of the expression:
\[ D_x \left( 4x^{-\frac{1}{3}} + \frac{6}{x^{\frac{4}{3}}} \right) = \, \text{[Solution]} \]

**Explanation:**

The expression involves finding the derivative of two terms:

1. \( 4x^{-\frac{1}{3}} \)
2. \( \frac{6}{x^{\frac{4}{3}}} \) which can also be written as \( 6x^{-\frac{4}{3}} \)

Apply the power rule for differentiation, which states: If \( f(x) = ax^n \), then \( f'(x) = anx^{n-1} \).

**Notes:**

- Evaluate each term separately.
- Simplify the expressions to make the derivative calculation straightforward.
Transcribed Image Text:**Title: Calculating the Derivative of a Function** **Objective:** Find the derivative of the given mathematical expression. **Expression:** Given: \[ D_x \left( 4x^{-\frac{1}{3}} + \frac{6}{x^{\frac{4}{3}}} \right) \] **Task:** Calculate the derivative of the expression: \[ D_x \left( 4x^{-\frac{1}{3}} + \frac{6}{x^{\frac{4}{3}}} \right) = \, \text{[Solution]} \] **Explanation:** The expression involves finding the derivative of two terms: 1. \( 4x^{-\frac{1}{3}} \) 2. \( \frac{6}{x^{\frac{4}{3}}} \) which can also be written as \( 6x^{-\frac{4}{3}} \) Apply the power rule for differentiation, which states: If \( f(x) = ax^n \), then \( f'(x) = anx^{n-1} \). **Notes:** - Evaluate each term separately. - Simplify the expressions to make the derivative calculation straightforward.
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