Question

differentiate the following function w.r.t.x 3x+2/(x+5)(2x+1)+3

Answer 1

Hey

We use the Quotient Rule -->
$\frac{d}{dx} \frac{3x + 2}{(x + 5)(2x + 1) + 3} \\ \\ = \frac{((x + 5)(2x + 1) + 3 )(3) - (3x + 2)(4x + 11)}{{(x + 5)(2x + 1) + 3)}^{2} }$
--> And we expand this to get the required D.C.-->
$\frac{ - 6 {x}^{2} - 8x + 2 }{ {(2 {x}^{2} + 11x + 8) }^{2} }$