Question

Find the derivative of the following function.1/(x2 - 1) (x2 + 5x+2)

Answer 1

we have the following:

`y=(1)/((x^2-1)(x^2+5x+2))`

derivate:

`\begin{gathered} y^(\prime)=((d)/(dx)\lbrack(x^2-1)\rbrack\cdot(x^2+5x+2)+(d)/(dx)\lbrack(x^2+5x+2)\rbrack(x^2-1))/((x^2-1)^2(x^2+5x+2)^2) \\ y´=(2x\cdot(x^2+5x+2)+(2x+5)\cdot(x^2-1))/((x^2-1)^2(x^2+5x+2)^2) \\ y^(\prime)=(2x^3+10x^2+4x+2x^3-2x+5x^2-5)/((x^2-1)^2(x^2+5x+2)^2) \\ y^(\prime)=(4x^3+15x^2+2x-5)/((x^2-1)^2(x^2+5x+2)^2) \end{gathered}`