Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

f(x) =
=
Find f'(x) and f''(x).
+
EL
ALEHER
24
) (
f''(x) = {
Epe

Fx Find Fx And Fx EL ALEHER 24 Fx Epe class=

Sagot :

LammettHash

To make things easier, first rewrite

f(x) = x / (x + 7/x) = x ² / (x ² + 7)

i.e. multiply f by x/x, which is valid because x can't be 0 anyway as it's outside the domain of f.

Now, by the quotient and chain rules, we get

f '(x) = ((x ² + 7) (x ²)' - x ² (x ² + 7)') / (x ² + 7)²

… = (2x (x ² + 7) - x ² (2x)) / (x ² + 7)²

… = (2x ³ + 14x - 2x ³) / (x ² + 7)²

… = 14x / (x ² + 7)²

f ''(x) = ((x ² + 7)² (14x)' - (14x) ((x ² + 7)²)') / ((x ² + 7)²)²

… = (14 (x ² + 7)² - (14x) (2 (x ² + 7)² (x ² + 7)')) / (x ² + 7)⁴

… = (14 (x ² + 7)² - (14x) (2 (2x) (x ² + 7)²)) / (x ² + 7)⁴

… = (14 (x ² + 7)² - 4x (14x) (x ² + 7)²) / (x ² + 7)⁴

… = 14 (x ² + 7)² (1 - 4x) / (x ² + 7)⁴

… = 14 (1 - 4x) / (x ² + 7)²

… = (14 - 56x) / (x ² + 7)²

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.