Question

y= (x^2 + 1 ) (x+2) then differentiate with respect to x
that is dy / dx​

Answer 1

ANSWER :–

▪︎${ \boxed { \bold{ \dfrac{dy}{dx} = 3 {x}^{2} + 4x + 1 }}}$

EXPLANATION :–

GIVEN :–

▪︎ A function y = (x² + 1)(x + 2)

TO FIND :–

${ \bold{ \dfrac{dy}{dx} = ? }}$

SOLUTION :–

▪︎ Function –

$\\ \implies \: { \bold{y = ( {x}^{2} + 1)(x + 2)}}$

▪︎ Now Differentiate with respect to 'x' –

$\\ \implies \: { \bold{ \dfrac{dy}{dx} = ( {x}^{2} + 1).(1) + (2x)(x + 2)}}$

$\\ \implies{ \bold{ \dfrac{dy}{dx} = {x}^{2} + 1 + 2 {x}^{2} + 4x }}$

$\\ \implies{ \boxed { \bold{ \dfrac{dy}{dx} = 3 {x}^{2} + 4x + 1 }}}$

USED FORMULA :–

$\\ { \bold{ (1) \dfrac{d(u.v)}{dx} = u \dfrac{dv}{dx} + v \dfrac{du}{dx} }}$

$\\ { \bold{ (2) \dfrac{d( {x}^{n} )}{dx} = \: n {x}^{n - 1} }}$

Answer 2

Answer:

dy/dx=(x^2+1)+(x+2)2x

Explanation:

uv=uv'+vu'

u=(x^2+1)

u'=2x

v=(x+2)

v'=1

dy/dx=uv'+vu'

=(x^2+1)(1)+(x+2)(2x)

=(x^2+2)+(x+2)2x