Question

question
if (t(x)=\frac{0.9e^{x}}{ln(x)}), find (t(5)) to the nearest tenth.
provide your answer below:

Explanation:

Step1: Apply quotient - rule

$t'(x)=\frac{0.9e^{x}\cdot\frac{1}{x}-\ln(x)\cdot0.9e^{x}}{(\ln(x))^{2}}$

Step2: Simplify

$t'(x)=\frac{0.9e^{x}(\frac{1}{x}-\ln(x))}{(\ln(x))^{2}}$

Step3: Substitute $x = 5$

$t'(5)=\frac{0.9e^{5}(\frac{1}{5}-\ln(5))}{(\ln(5))^{2}}$
$t'(5)\approx - 48.7$

Answer:

$-48.7$