got stuck in 1 and 2 1 Diferentiate each of the following functions2. Use the derivatives of each of the functions in problem (1) to find where each funtimhas horizontal tangents. You might need to simply the derivative of each function

Answered: 1 Drentiate each of the folowing…

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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got stuck in 1 and 2

1 Diferentiate each of the following functions
2. Use the derivatives of each of the functions in problem (1) to find where each funtim
has horizontal tangents. You might need to simply the derivative of each function

Expert Solution

Step 1

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Differentiation:

The process of finding the derivative of a function is called Differentiation.

Rules of differentiation:

The derivative of Sum and Difference:
The derivative of the sum (difference) of two functions is equal to the sum (difference) of their
derivatives. i.e.

if $f (x) = g (x) \pm h (x)$ , then $f' (x) = g' (x) \pm h' (x)$

Product function Rule: If $f (x) = g (x) \cdot h (x)$ , then $f' (x) = g' (x) \cdot h (x) + g (x) \cdot h' (x)$
Derivative of the Quotient of two Functions (Quotient Rule): If $f (x) = \frac{g (x)}{h (x)}$ , where $g (x)$ and $h (x)$ are both differentiable at $x$ and $h (x) \neq 0$ then
$f' (x) = \frac{g' (x) \cdot h (x) - g (x) \cdot h' (x)}{{[h (x)]}^{2}}$