Question

Differentiate with product rule

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Answer 1

`{ \boxed{ \bf{ (dy)/(dx) = v (du)/(dx) + u (dv)/(dx) }}}`

u = ( x + 1 )

v = ( 2x + 5 )²

`{ \tt{ (dy)/(dx) = {(2x + 5) {}^(4) .(1) + (x + 1).(2)(2x + 5) {}^(3) } }} \\ = { \tt{ {(2x + 5)}^(3) ((2x + 5) +(2x + 2) }} \\ = { \tt{ (dy)/(dx) = {(2x + 5)}^(3)(4x + 7) }}`