Question

Find dy/dx when y=logx/x

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{y=\dfrac{logx}{x}}$

$\underline{\textbf{To find:}}$

$\mathsf{\dfrac{dy}{dx}}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Quotient rule:}}$

$\boxed{\mathsf{\dfrac{d\left(\dfrac{u}{v}\right)}{dx}=\dfrac{v\;\dfrac{du}{dx}-u\;\dfrac{dv}{dx}}{v^2}}}$

$\mathsf{Consider,}$

$\mathsf{y=\dfrac{logx}{x}}$

$\textsf{Differentiate with respect to 'x,}$

$\textsf{by quotient rule}$

$\mathsf{\dfrac{dy}{dx}=\dfrac{x\;\dfrac{d(logx)}{dx}-logx\;\dfrac{d(x)}{dx}}{x^2}}$

$\mathsf{\dfrac{dy}{dx}=\dfrac{x\;\left(\dfrac{1}{x}\right)-logx\;(1)}{x^2}}$

$\implies\boxed{\mathsf{\dfrac{dy}{dx}=\dfrac{1-logx}{x^2}}}$

$\underline{\textbf{Find more:}}$

If y = √1+cos 2X /√1-cos 2X ,find dy/dx.https://brainly.in/question/4712606