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)#