How do you find the derivative of $e^(4x)/x$ ?

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Answer 1 · 2017-02-24T17:07:12

$(df)/(dx)=e^(4x)/x^2(4x-1)$

We can use quotient rule, which states that

if $f(x)=(g(x))/(h(x))$

then $(df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2$

Here we have $f(x)=e^(4x)/x$ , where $g(x)=e^(4x)$ and $h(x)=x$

and therefore $(df)/(dx)=(4e^(4x)xx x-1xxe^(4x))/x^2$

= $e^(4x)/x^2(4x-1)$

How do you find the derivative of e^(4x)/xe^(4x)/x?