How do you find the derivative of e^(4x)/xe4xx?

1 Answer
Feb 24, 2017

(df)/(dx)=e^(4x)/x^2(4x-1)dfdx=e4xx2(4x1)

Explanation:

We can use quotient rule, which states that

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

then (df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2dfdx=dgdx×h(x)dhdx×g(x)(h(x))2

Here we have f(x)=e^(4x)/xf(x)=e4xx, where g(x)=e^(4x)g(x)=e4x and h(x)=xh(x)=x

and therefore (df)/(dx)=(4e^(4x)xx x-1xxe^(4x))/x^2dfdx=4e4x×x1×e4xx2

= e^(4x)/x^2(4x-1)e4xx2(4x1)