Question

if y=(x power 2+1) (2x-1) find dy/ dx​

Answer 1

We have to differentiate the following expression :-

$\rm y = ({x}^{2} + 1)(2x - 1)$

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

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

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

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

$\rm \longrightarrow \dfrac{dy}{dx} = 6{x}^{2} - 2x +2$

Answer :-

$\rm \dfrac{dy}{dx} = 6{x}^{2} - 2x +2$

Additional Information :-

d(e^x)/dx = e^x

d(x^n)/dx = n x^(n-1)

d(ln x)/dx = 1/x

d(sin x)/dx = cos x

d(cos x)/dx = - sin x

d(tan x)/dx = sec² x

d(sec x)/dx = tan x * sec x

d(cot x)/dx = - cosec²x

d(cosec x)/dx = - cosec x * cot x