Question

find dy/dx ( product rule) y=(2x²+3) (4x+1)​

Answer 1

Answer:

24x² + 4x + 12

Step-by-step explanation:

(note: the symbol ' refers to derivative)

y' = (2x²+3) (4x+1)​

product rule: (uv)' = uv' + vu'

((2x²+3) (4x+1)​)' = (2x²+3) (4) +  (4x+1) (4x)

=  4(2x²+3) +  4x(4x+1)

= 8x² + 12 + 16x² + 4x

= 24x² + 4x + 12

Answer 2

$\frac{d}{dx}((2x^2+3)(4x+1))=\frac{d}{dx}(2x^2+3)*(4x+1)+\frac{d}{dx}(4x+1)*(2x^2+3)\\\\\frac{d}{dx}((2x^2+3)(4x+1))=(4x)(4x+1)+(4)(2x^2+3)\\\\\frac{d}{dx}((2x^2+3)(4x+1))=(16x^2+4x)+(8x^2+12)\\\\\frac{d}{dx}((2x^2+3)(4x+1))=24x^2+4x+12$

We simply followed according to what the product rule said. Hope this answer helped.