Question

find the derivative of the function.

$y = \frac{7x^{2}+2}{x^{2}+5}$

$y = \square$

Explanation:

Step1: Identify the quotient rule

For \(y = \frac{u}{v}\), \(y^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}\). Here \(u = 7x^{2}+2\), \(u^\prime=14x\); \(v = x^{2}+5\), \(v^\prime = 2x\).

Step2: Substitute into the quotient rule formula

$$
LATEXBLOCK0
$$

Step3: Simplify the numerator

$$
LATEXBLOCK1
$$

Answer:

\(\frac{66x}{(x^{2}+5)^{2}}\)