How do I find the derivative of $f(x)= (7lnx)/(4x)$ ?

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Answer 1 · 2018-03-31T21:32:00

$f'(x)=(7(1-lnx))/(4x^2)$

Applying the quotient rule yields

$f'(x)=(4x*d/dx7lnx-7lnx*d/dx4x)/(4x^2)$

(Recalling that $d/dxlnx=1/x$ ):

$f'(x)=((4(7)x)/x-7(4)(lnx))/(16x^2)$

$f'(x)=(28-28lnx)/(16x^2)$

$f'(x)=(28(1-lnx))/(16x^2)$

$f'(x)=(7(1-lnx))/(4x^2)$

How do I find the derivative of f(x)= (7lnx)/(4x)f(x)= (7lnx)/(4x)?