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

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

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Answer 1 · 2017-02-24T17:07:12

$\frac{d f}{d x} = \frac{e^{4 x}}{x^{2}} (4 x - 1)$ $(df)/(dx)=e^(4x)/x^2(4x-1)$

Explanation:

We can use quotient rule, which states that

if $f (x) = \frac{g (x)}{h (x)}$ $f(x)=(g(x))/(h(x))$

then $\frac{d f}{d x} = \frac{\frac{d g}{d x} \times h (x) - \frac{d h}{d x} \times g (x)}{{(h (x))}^{2}}$ $(df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2$

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

and therefore $\frac{d f}{d x} = \frac{4 e^{4 x} \times x - 1 \times e^{4 x}}{x^{2}}$ $(df)/(dx)=(4e^(4x)xx x-1xxe^(4x))/x^2$

= $\frac{e^{4 x}}{x^{2}} (4 x - 1)$ $e^(4x)/x^2(4x-1)$

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

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