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Question Number 174442 by oustmuchiya@gmail.com last updated on 01/Aug/22

Answered by floor(10²Eta[1]) last updated on 01/Aug/22

$$\mathrm{a})$$$${\mathrm{y}}^{\prime }=\frac{{(\mathrm{x}+1)}^4}{2\sqrt{\mathrm{x}-1}}+4{(\mathrm{x}+1)}^3\sqrt{\mathrm{x}-1}$$$${(\mathrm{x}+1)}^3[\frac{\mathrm{x}+1}{2\sqrt{\mathrm{x}-1}}+4\sqrt{\mathrm{x}-1}]$$$${(\mathrm{x}+1)}^3\left(\frac{9\mathrm{x}-7}{2\sqrt{\mathrm{x}-1}}\right)$$$$\mathrm{b})$$$${\mathrm{y}}^{\prime }=6(3\mathrm{x}-1){(2\mathrm{x}+3)}^3+6{(2\mathrm{x}+3)}^2{(3\mathrm{x}-1)}^2$$$$=6(3\mathrm{x}-1){(2\mathrm{x}+3)}^2[(2\mathrm{x}+3)+(3\mathrm{x}-1)]$$$$=6(3\mathrm{x}-1){(2\mathrm{x}+3)}^2(5\mathrm{x}+2)$$

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