Question

y=6x²+1/x²-2x find dy/dx​

Answer 1

ANSWER :–

$\\ \bf \longrightarrow \dfrac{dy}{dx} =12x-\dfrac{2}{{x}^{3}}- 2$

EXPLANATION :–

GIVEN :–

• Function y = 6x² + 1/x² - 2x.

TO FIND :–

• dy/dx = ?

SOLUTION :–

$\\ \bf \implies y = 6 {x}^{2} + \dfrac{1}{{x}^{2}} - 2x$

• We should write this as –

$\\ \bf \implies y = 6 {x}^{2} + {x}^{ - 2} - 2x$

• Using identity –

$\\ \bf \implies \dfrac{d( {x}^{n})}{dx} = n {x}^{n - 1}$

• Now Differentiate with respect to 'x' –

$\\ \bf \implies \dfrac{dy}{dx} = 6 \dfrac{d({x}^{2})}{dx}+ \dfrac{d({x}^{ - 2})}{dx} - 2 \dfrac{d(x)}{dx}$

$\\ \bf \implies \dfrac{dy}{dx} = 6(2 {x}^{2 - 1} )+( - 2)( {x}^{ - 2 - 1})- 2 (1. {x}^{1 - 1})$

$\\ \bf \implies \dfrac{dy}{dx} = 6(2 {x}^{1} )+( - 2)( {x}^{ - 3})- 2 (1. {x}^{0})$

$\\ \bf \implies \dfrac{dy}{dx} = 6(2x )- 2( {x}^{ - 3})- 2 (1)$

$\\ \bf \implies \dfrac{dy}{dx} =12x- 2{x}^{ - 3}- 2$

$\\ \bf \implies \large{ \boxed{ \bf \dfrac{dy}{dx} =12x-\dfrac{2}{{x}^{3}}- 2}}$

Answer 2

$ANSWER :–</p><p>\begin{gathered}\\ \bf \longrightarrow \dfrac{dy}{dx} =12x-\dfrac{2}{{x}^{3}}- 2\\\end{gathered}⟶dxdy=12x−x32−2</p><p>EXPLANATION :–</p><p>GIVEN :–</p><p>• Function y = 6x² + 1/x² - 2x.</p><p>TO FIND :–</p><p>• dy/dx = ?</p><p>SOLUTION :–</p><p>\begin{gathered}\\ \bf \implies y = 6 {x}^{2} + \dfrac{1}{{x}^{2}} - 2x \\\end{gathered}⟹y=6x2+x21−2x</p><p>• We should write this as –</p><p>\begin{gathered}\\ \bf \implies y = 6 {x}^{2} + {x}^{ - 2} - 2x \\\end{gathered}⟹y=6x2+x−2−2x</p><p>• Using identity –</p><p>\begin{gathered}\\ \bf \implies \dfrac{d( {x}^{n})}{dx} = n {x}^{n - 1} \\\end{gathered}⟹dxd(xn)=nxn−1</p><p>• Now Differentiate with respect to 'x' –</p><p>\begin{gathered}\\ \bf \implies \dfrac{dy}{dx} = 6 \dfrac{d({x}^{2})}{dx}+ \dfrac{d({x}^{ - 2})}{dx} - 2 \dfrac{d(x)}{dx} \\\end{gathered}⟹dxdy=6dxd(x2)+dxd(x−2)−2dxd(x)</p><p>\begin{gathered}\\ \bf \implies \dfrac{dy}{dx} = 6(2 {x}^{2 - 1} )+( - 2)( {x}^{ - 2 - 1})- 2 (1. {x}^{1 - 1}) \\\end{gathered}⟹dxdy=6(2x2−1)+(−2)(x−2−1)−2(1.x1−1)</p><p>\begin{gathered}\\ \bf \implies \dfrac{dy}{dx} = 6(2 {x}^{1} )+( - 2)( {x}^{ - 3})- 2 (1. {x}^{0}) \\\end{gathered}⟹dxdy=6(2x1)+(−2)(x−3)−2(1.x0)</p><p>\begin{gathered}\\ \bf \implies \dfrac{dy}{dx} = 6(2x )- 2( {x}^{ - 3})- 2 (1) \\\end{gathered}⟹dxdy=6(2x)−2(x−3)−2(1)</p><p>\begin{gathered}\\ \bf \implies \dfrac{dy}{dx} =12x- 2{x}^{ - 3}- 2\\\end{gathered}⟹dxdy=12x−2x−3−2</p><p>\begin{gathered}\\ \bf \implies \large{ \boxed{ \bf \dfrac{dy}{dx} =12x-\dfrac{2}{{x}^{3}}- 2}}\\\end{gathered}⟹dxdy=12x−x32−2$