Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 201764 by hardmath last updated on 11/Dec/23

$$1.\mathrm{y}=\mathrm{tgx}-\mathrm{ctgx}\to {\mathrm{y}}^{{}^{\prime }}=?$$$$2.\mathrm{y}=(1+{\mathrm{x}}^2)\mathrm{arctgx}\to {\mathrm{y}}^{{}^{\prime }}=?$$$$3.\mathrm{y}={\cos }^4\mathrm{x}\to {\mathrm{y}}^{{}^{\prime }}=?$$$$4.\{\begin{array}{l}\mathrm{x}=2\mathrm{t}\\ \mathrm{y}={3\mathrm{t}}^2-5\mathrm{t}\end{array}\to {\mathrm{x}}^{{}^{\prime }},{\mathrm{y}}^{{}^{\prime }}=?$$

Answered by Calculusboy last updated on 11/Dec/23

$$\mathit{S}\mathit{o}\mathit{l}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}:\left(1\right)\mathit{y}=\mathit{t}\mathit{g}\mathit{x}-\mathit{c}\mathit{t}\mathit{g}\mathit{x}\mathit{i}\mathit{f}\mathit{t}\mathit{g}\mathit{x}=\mathit{t}\mathit{a}\mathit{n}\mathit{x}\mathit{a}\mathit{n}\mathit{d}\mathit{c}\mathit{t}\mathit{g}\mathit{x}=\mathit{c}\mathit{o}\mathit{t}\mathit{x}$$$${\mathit{y}}^{\prime }={\mathit{s}\mathit{e}\mathit{c}}^2\mathit{x}+{\mathit{c}\mathit{o}\mathit{s}\mathit{e}\mathit{c}}^2\mathit{x}$$$$\left(2\right)\mathit{b}\mathit{y}\mathit{u}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{p}\mathit{r}\mathit{o}\mathit{d}\mathit{u}\mathit{c}\mathit{t}\mathit{r}\mathit{u}\mathit{l}\mathit{e}\mathit{i}\mathit{f}\mathit{t}\mathit{g}\mathit{x}=\mathit{t}\mathit{a}\mathit{n}\mathit{x}$$$${\mathit{y}}^{\prime }=[(1+{\mathit{x}}^2)\frac{\mathit{d}}{\mathit{d}\mathit{x}}\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{g}\mathit{x}+\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{g}\mathit{x}\frac{\mathit{d}}{\mathit{d}\mathit{x}}\left(1{+}^2\right)]$$$${\mathit{y}}^{\prime }=[(1+{\mathit{x}}^2)\times \frac{1}{1+{\mathit{x}}^2}+2\mathit{x}\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{g}\mathit{x}]$$$${\mathit{y}}^{\prime }=1+2\mathit{x}\mathit{a}\mathit{r}\mathit{c}\mathit{t}\mathit{g}\mathit{x}$$$$\left(3\right)\mathit{y}={\mathit{c}\mathit{o}\mathit{s}}^4\mathit{x}\mathit{l}\mathit{e}\mathit{t}\mathit{p}=\mathit{c}\mathit{o}\mathit{s}\mathit{x}$$$$\mathit{y}={\left(\mathit{c}\mathit{o}\mathit{s}\mathit{x}\right)}^4\frac{\mathit{d}\mathit{p}}{\mathit{d}\mathit{x}}=-\mathit{s}\mathit{i}\mathit{n}\mathit{x}$$$$\mathit{y}={\mathit{p}}^4\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{p}}=4{\mathit{p}}^3\iff {\mathit{y}}^{\prime }=4{\mathit{c}\mathit{o}\mathit{s}}^3\mathit{x}\times -\mathit{s}\mathit{i}\mathit{n}\mathit{x}=-4{\mathit{c}\mathit{o}\mathit{s}}^3\mathit{x}\mathit{s}\mathit{i}\mathit{n}\mathit{x}$$$${\mathit{y}}^{\prime }=-4{\mathit{c}\mathit{o}\mathit{s}}^3\mathit{x}\mathit{s}\mathit{i}\mathit{n}\mathit{x}$$$$$$$$$$$$$$

Commented by Calculusboy last updated on 12/Dec/23

$$\mathit{y}\mathit{o}\mathit{u}\mathit{a}\mathit{r}\mathit{e}\mathit{w}\mathit{e}\mathit{l}\mathit{c}\mathit{o}\mathit{m}\mathit{e}$$

Commented by hardmath last updated on 12/Dec/23

$$\mathrm{thank}\mathrm{you}\mathrm{ser}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com