[tex]f(x)=(x^2-1)\cdot(\sqrt{x+1}\, \\ \, f\prime(x)=2x\sqrt{x+1}+\frac{(x^2-1)}{2\sqrt{x+1}\, \\ \, \frac{4x(x+1)\sqrt{x+1}+(x+1)(x-1)}{2\sqrt{x+1}}[/tex]
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[tex]f(x) = (x^2-1)(\sqrt{x+1})[/tex]
[tex]\left[x^2-1\right]^\prime = 2x[/tex]
[tex]\left[\sqrt{x+1}\right]^\prime = \sqrt u ^\prime \cdot u^\prime,\,\,\,\text{der}\,\, u = x+1[/tex]
[tex]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\frac{1}{2\sqrt{x+1}}[/tex]
[tex]f^\prime(x) = 2x(\sqrt{x+1})+(x^2-1)\cdot\frac{1}{2\sqrt{x+1}}[/tex]
[tex]f(x) = (x^2-1)(\sqrt{x+1})[/tex]
[tex]\left[x^2-1\right]^\prime = 2x[/tex]
[tex]\left[\sqrt{x+1}\right]^\prime = \sqrt u ^\prime \cdot u^\prime,\,\,\,\text{der}\,\, u = x+1[/tex]
[tex]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\frac{1}{2\sqrt{x+1}}[/tex]
[tex]f^\prime(x) = 2x(\sqrt{x+1})+(x^2-1)\cdot\frac{1}{2\sqrt{x+1}}[/tex]