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Find the derivative of the following function. 5 -- 2 y = 7x + 10x y'=0 1 + X 12_ -4

Find the derivative of the following function. 5 -- 2 y = 7x + 10x y'=0 1 + X 12_ -4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Find the derivative of the following function. \[ y = 7x - \frac{5}{2} + 10x - \frac{1}{2} + x^{12} - 4 \] **Solution:** To find the derivative \( y' \), differentiate each term of the function with respect to \( x \): - The derivative of \( 7x \) is 7. - The derivative of a constant \( -\frac{5}{2} \) is 0. - The derivative of \( 10x \) is 10. - The derivative of a constant \( -\frac{1}{2} \) is 0. - The derivative of \( x^{12} \) is \( 12x^{11} \) using the power rule. - The derivative of a constant \(-4\) is 0. Combine the terms to get the derivative: \[ y' = 7 + 10 + 12x^{11} \] Therefore, \[ y' = 12x^{11} + 17 \]
Transcribed Image Text:**Problem Statement:** Find the derivative of the following function. \[ y = 7x - \frac{5}{2} + 10x - \frac{1}{2} + x^{12} - 4 \] **Solution:** To find the derivative \( y' \), differentiate each term of the function with respect to \( x \): - The derivative of \( 7x \) is 7. - The derivative of a constant \( -\frac{5}{2} \) is 0. - The derivative of \( 10x \) is 10. - The derivative of a constant \( -\frac{1}{2} \) is 0. - The derivative of \( x^{12} \) is \( 12x^{11} \) using the power rule. - The derivative of a constant \(-4\) is 0. Combine the terms to get the derivative: \[ y' = 7 + 10 + 12x^{11} \] Therefore, \[ y' = 12x^{11} + 17 \]
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