Question

find f(x).
f(x)=\frac{e^{x}}{6x^{2}+5}
f(x)=square

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}$. Here, $u = e^{x}$ and $v=6x^{2}+5$.

Step2: Find $u^\prime$ and $v^\prime$

The derivative of $u = e^{x}$ is $u^\prime=e^{x}$ (since the derivative of $e^{x}$ with respect to $x$ is $e^{x}$), and the derivative of $v = 6x^{2}+5$ is $v^\prime = 12x$ (using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$).

Step3: Apply the quotient - rule

$$
LATEXBLOCK0
$$

Answer:

$\frac{e^{x}(6x^{2}-12x + 5)}{(6x^{2}+5)^{2}}$