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Question Number 198953 by ArifinTanjung last updated on 26/Oct/23

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{3\mathrm{x}-5}{2\mathrm{x}+1}\to {\mathrm{f}}^{{}^{\prime }}\left(\mathrm{x}\right)=....?$$

Answered by Rasheed.Sindhi last updated on 26/Oct/23

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{3\mathrm{x}-5}{2\mathrm{x}+1}\to {\mathrm{f}}^{{}^{\prime }}\left(\mathrm{x}\right)=....?$$$${\left(\frac{u}{v}\right)}^{{}^{\prime }}=\frac{v{u}^{\prime }-u{v}^{\prime }}{v^2}$$$$u=3x-5\Rightarrow u^{\prime }=3$$$$v=2x+1\Rightarrow v^{\prime }=2$$$$f{}^{\prime }\left(x\right)=\frac{(2x+1)\left(3\right)-(3x-5)\left(2\right)}{{(2x+1)}^2}$$$$=\frac{6x+3-6x+10}{{(2x+1)}^2}$$$$=\frac{13}{{(2x+1)}^2}$$

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