Question

find the dy/dx of y=4x- 1/2x

Answer 1

Answers:

check your questions as well as your answer

thank you..

Answer 2

Question:

$\\\quad\bullet\quad\rm y = \dfrac{4x-1}{2x}$

find dy/dx

Solution:

$\\\\\quad\longrightarrow\quad\rm y = \dfrac{4x-1}{2x}$

$\\\\\quad\longrightarrow\quad\rm \dfrac{dy}{dx} = \dfrac{2x \times \dfrac{d}{dx}\bigg(4x-1\bigg)-\bigg(4x-1\bigg)\times \dfrac{d}{dx}\bigg(2x\bigg) }{\bigg(2x\bigg)^{2} }$

$\\\quad\longrightarrow\quad\rm \dfrac{dy}{dx} = \dfrac{(2x )(4)-(4-1)(2)}{4x^{2} }$

$\\\quad\longrightarrow\quad\rm \dfrac{dy}{dx} = \dfrac{8x-8x+2}{4x^{2} }$

$\\\quad\longrightarrow\quad\rm \dfrac{dy}{dx} = \dfrac{2}{4x^{2} }$

$\\\quad\therefore\quad \boxed{\rm \dfrac{dy}{dx} = \dfrac{1}{2x^{2} } }$

Formulas Applied:

$\\\quad\bullet\quad\rm \dfrac{d}{dx}\bigg[\dfrac{u}{v}\bigg] = \dfrac{v\dfrac{du}{dx}-u\dfrac{dv}{dx} }{v^{2} }$

$\\\quad\bullet\quad\rm \dfrac{d}{dx}\bigg(ax\bigg) = a$

$\\\quad\bullet\quad\rm \dfrac{d}{dx}\bigg(c\bigg) = 0$

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