Question

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Differentiate the given expression using the first principle of differentiation ~

$\dfrac{d}{dx} ( \frac{tan(x)}{x} )$



Points to be noted :

➢ I need the full solution

➢ you can use trigonometric formulas and first principle of derivative only.

➢ Don't Answer if you don't know !

Thanks for your help ~ ​

Answer 1

$\\ \boxed{\sf \dfrac{d}{dx}(\dfrac{u}{v})=v\dfrac{du}{dx}-u\dfrac{dv}{dx}}$

Now

$\\ \sf\longmapsto \dfrac{d}{dx}(\dfrac{tanx}{x})$

$\\ \sf\longmapsto x\dfrac{d}{dx}(tanx)-tanx\dfrac{dx}{dx}$

$\\ \sf\longmapsto \dfrac{sec^2x.x-tanx.1}{x^2}$

$\\ \sf\longmapsto\dfrac{ \dfrac{x}{cos^2x}-tanx}{x^2}$

$\\ \sf\longmapsto \dfrac{\dfrac{x^2}{cos^2x}-\dfrac{sinx}{cosx}}{x^2}$

$\\ \sf\longmapsto \dfrac{x-sinxcosx}{x^2cos^2x}$

Answer 2

Hope that the attachment helps you!!