Question

if y=xtan x+(tan x)x ,then find dy/dx​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer

• 2(tanx+x.sec²x

Given

• y = x tanx + (tanx) x

To Find

• dy/dx

Solution

y = x tanx + (tanx) x

⇒ y = x tanx + x tanx

⇒ y = 2x tanx

Differentiating y with respect to x on both sides , we get ,

$\implies \tt \dfrac{dy}{dx}=\dfrac{d}{dx}(2xtanx)\\\\\implies \tt \dfrac{dy}{dx}=2\dfrac{d}{dx}(xtanx)\\\\\tt Since\ we\ know\ that\ \dfrac{d}{dx}(uv)=v\dfrac{du}{dx}+u\dfrac{dv}{dx}\\\\\implies \tt \dfrac{dy}{dx}=2[tanx.\dfrac{dx}{dx}+x\dfrac{d}{dx}(tanx)]\\\\\implies \tt \dfrac{dy}{dx}=2[tanx+x.sec^2x]$