let\nf(x)=ln(x^{4})\nf(x)=\frac{4x^{3}}{x^{4}}\nf(e^{4})=\text{empty box}

let\nf(x)=ln(x^{4})\nf(x)=\frac{4x^{3}}{x^{4}}\nf(e^{4})=\text{empty box}

let\nf(x)=ln(x^{4})\nf(x)=\frac{4x^{3}}{x^{4}}\nf(e^{4})=\text{empty box}

Answer

Explanation:

Step1: Simplify the derivative expression

We have $f'(x)=\frac{4x^{3}}{x^{4}}$, and by the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we can simplify it to $f'(x)=\frac{4}{x}$ ($x\neq0$).

Step2: Substitute $x = e^{4}$

Substitute $x = e^{4}$ into $f'(x)=\frac{4}{x}$, we get $f'(e^{4})=\frac{4}{e^{4}}$.

Answer:

$\frac{4}{e^{4}}$