Question

if $s(x)=\frac{90x^{4}}{2^{x}}$ what is $s(x)$? select the correct answer below: $s(x)=\frac{90(x^{4})(2^{x})(ln 2)-90(2^{x})(4x^{3})}{2^{2x}}$ $s(x)=\frac{90(4x^{3})}{(2^{x})(ln 2)}$ $s(x)=\frac{90(2^{x})(4x^{3})-90(x^{4})(x)(2^{x - 1})}{2^{2x}}$ $s(x)=\frac{90(2^{x})(4x^{3})-90(x^{4})(2^{x})(ln 2)}{2^{2x}}$

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 90x^{4}$, $u'=90\times4x^{3}=360x^{3}$, $v = 2^{x}$, and $v'=2^{x}\ln2$.

Step2: Substitute into quotient - rule

$s'(x)=\frac{360x^{3}\cdot2^{x}-90x^{4}\cdot2^{x}\ln2}{(2^{x})^{2}}=\frac{90(2^{x})(4x^{3})-90(x^{4})(2^{x})(\ln2)}{2^{2x}}$

Answer:

$\text{The last option: }s'(x)=\frac{90(2^{x})(4x^{3})-90(x^{4})(2^{x})(\ln2)}{2^{2x}}$