Question

find the derivative of (6x ^ 2 + 4x + 5)(2x + 3)​

Answer 1

Answer:

(12x+4)(2x+3)+(6x^2 +4x+5)(2)

Step-by-step explanation:

we have to use chain rule here

(6x^2+4x+5)' (2x+3) + (6x^2+4x+5) (2x+3)'

(12x+4+0) (2x+3) + (6x^2+4x+5) (2)

Answer 2

$\rm \longrightarrow \: \dfrac{d\bigg(( 6 {x}^{2} + 4x + 5)(2x + 3) \bigg)}{dx} \\ \\ \\ \rm \longrightarrow \: (2x + 3) \: \dfrac{d\bigg(6 {x}^{2} + 4x + 5\bigg)}{dx} + (6 {x}^{2} + 4x + 5)\dfrac{d\bigg(2x + 3\bigg)}{dx}\\ \\ \\ \rm \longrightarrow \: (2x + 3)(12{x}+ 4 ) \: + (6 {x}^{2} + 4x + 5)2\\ \\ \\ \rm \longrightarrow \: 24 {x}^{2} + 8x + 36x + 12 \: + (6 {x}^{2} + 4x + 5)2\\ \\ \\ \rm \longrightarrow \: 24 {x}^{2} + 8x + 36x + 12 \: + 12{x}^{2} + 8x + 10\\ \\ \\ \rm \longrightarrow \: 36 {x}^{2} + 52x +22$

Learn more :-

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