Hoe do you differentiate f(x)=ln(e^(4x)/x) f(x)=ln(e4xx)?

1 Answer
Apr 18, 2018

4-1/x41x

Explanation:

Use log laws to expand
f (x)=ln [(e^(4x))/x]f(x)=ln[e4xx]
=ln ((e^(4x))-ln (x)=ln((e4x)ln(x)
=4x-lnx=4xlnx
Differentiating with respect to x.
d/dx (f (x))=d/dx [(4x)-ln (x)]ddx(f(x))=ddx[(4x)ln(x)]
=d/dx(4x)-d/dx (ln (x))=ddx(4x)ddx(ln(x))
:.=4-1/x