We need to find the derivative of the following equation:
[tex]h(x)=|9x|\cos (2x)[/tex]
Since it's the product of two functions, we need to apply the following expression:
[tex]\begin{gathered} h(x)=f(x)\cdot g(x) \\ h^{\prime}(x)=f^{\prime}(x)\cdot g(x)+f(x)\cdot g^{\prime}(x) \end{gathered}[/tex]
Therefore we have:
[tex]\begin{gathered} h^{\prime}(x)=9\cdot\frac{9x}{|9x|}\cdot\cos (2x)-|9x|\cdot2\cdot\sin (2x) \\ h^{\prime}(x)=9\cdot\frac{9x}{9\cdot|x|}\cdot cos(2x)-|9x|\cdot2\cdot\sin (2x) \\ h^{\prime}(x)=\frac{9x}{|x|}\cdot\cos (2x)-|9x|\cdot2\cdot\sin (2x) \\ h^{\prime}(x)=\frac{9x\lbrack\cos (2x)-2x\cdot\sin (2x)\rbrack_{}}{|x|} \end{gathered}[/tex]
