Question

question 4. 1 point determine f(x) when f(x) = (8(4^x))/(3x^3). select the correct answer below: f = (6x)/(8(4^x)ln4) f = (3x^38(4^x)ln4 - 8(4^x)(6x))/(9x^4) f = (3x^38(x*4^(x - 1)) - 8(4^x)(6x))/(9x^4) f = (8(4^x)(6x)-(3x^3)8(4^x)ln4)/(9x^4)

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 8(4^{x})$ and $v = 3x^{2}$.
$u'=8(4^{x})\ln4$ and $v' = 6x$.

Step2: Calculate $f'(x)$

$f'(x)=\frac{8(4^{x})\ln4\cdot3x^{2}-8(4^{x})\cdot6x}{(3x^{2})^{2}}=\frac{8(4^{x})(3x^{2}\ln4 - 6x)}{9x^{4}}$.

Answer:

$\frac{8(4^{x})(3x^{2}\ln4 - 6x)}{9x^{4}}$