Estou com algumas dúvidas em algumas derivadas, não tem haver com regras de derivação mas sim com simplificações com radicais e exponenciais.
Um dos exercícios é este:
![f(x)= \sqrt[]{\frac{3}{{x}^{5}}}](/latexrender/pictures/6ece9ac4538bf0ea0bb303ed33d0a445.png "f(x)= \sqrt[]{\frac{3}{{x}^{5}}}")
A resolução do exercício é:
![f(x)=\frac{-5\sqrt[]{3}}{2\sqrt[]{{x}^{7}}}](/latexrender/pictures/fa5b5f0eb3f6ee8718cb2ba5438439dd.png "f(x)=\frac{-5\sqrt[]{3}}{2\sqrt[]{{x}^{7}}}")
Os meus cálculos:
= 
= ![\frac{1}{2\sqrt[]{}\frac{3}{{x}^{5}}}*\frac{-15}{{x}^{6}}](/latexrender/pictures/bffa052dc06a03638d03d8e1ec095f83.png "\frac{1}{2\sqrt[]{}\frac{3}{{x}^{5}}}*\frac{-15}{{x}^{6}}")
= ![\frac{-15}{2 {x}^{6}\sqrt[]{}\frac{3}{{x}^{5}}}](/latexrender/pictures/57bf6c56f7959b40bc1afbebbe32f813.png "\frac{-15}{2 {x}^{6}\sqrt[]{}\frac{3}{{x}^{5}}}")
Não sei simplificar mais do que isto
Onde posso ler sobre simplificações?
Obrigado
![f(x) = \sqrt[]{\frac{3}{x^5}}](/latexrender/pictures/9736ee344761b5f3cbc59336f7ea7e6b.png "f(x) = \sqrt[]{\frac{3}{x^5}}")
![f(x) = \frac{\sqrt[]{3}}{\sqrt[]{x^5}}](/latexrender/pictures/9b9aa23ebd46de8c990d06caa4d3369e.png "f(x) = \frac{\sqrt[]{3}}{\sqrt[]{x^5}}")
![f(x) = \frac{\sqrt[]{3}}{x^{\frac{5}{2}}}](/latexrender/pictures/6d903c691ac8f7912b2bb7730ac4a965.png "f(x) = \frac{\sqrt[]{3}}{x^{\frac{5}{2}}}")
![f(x)=\frac{\sqrt[]{3}}{{x}^{\frac{5}{2}}}](/latexrender/pictures/a7fe70ed13adb53b11e63c4e273e8291.png "f(x)=\frac{\sqrt[]{3}}{{x}^{\frac{5}{2}}}")
= ![\frac{\left(\sqrt[]{3} \right)\left({x}^{\frac{5}{2}}\right)-\left(\sqrt[]{3} \right)\left({x}^{\frac{5}{2}} \right)}{\left( {{x}^{\frac{5}{2}}} \right)^{2}}](/latexrender/pictures/19fcd510e9d8a56b089ccd2d2d2dd535.png "\frac{\left(\sqrt[]{3} \right)\left({x}^{\frac{5}{2}}\right)-\left(\sqrt[]{3} \right)\left({x}^{\frac{5}{2}} \right)}{\left( {{x}^{\frac{5}{2}}} \right)^{2}}")
= ![-\frac{\sqrt[]{3}*\frac{5}{2}{x}^{\frac{3}{2}}}{{x}^{\frac{10}{2}}}](/latexrender/pictures/2bebc543dd7855b63fd2ebcde4b9fbab.png "-\frac{\sqrt[]{3}*\frac{5}{2}{x}^{\frac{3}{2}}}{{x}^{\frac{10}{2}}}")
= ![\frac{\sqrt[]{3}*\frac{5}{2}\sqrt[]{{x}^{3}}}{{x}^{5}}](/latexrender/pictures/e3513e345066abbb46cdc92c2eb1e394.png "\frac{\sqrt[]{3}*\frac{5}{2}\sqrt[]{{x}^{3}}}{{x}^{5}}")
![f'(x) = \frac{g'(x).h(x) - g(x).h'(x)}{[h(x)]^2}](/latexrender/pictures/a029df2b00c3772431e006c0869d1ed8.png "f'(x) = \frac{g'(x).h(x) - g(x).h'(x)}{[h(x)]^2}")
![g(x) = \sqrt[]{3} =====> g'(x) = 0](/latexrender/pictures/771cf72235012990685b173d5f3c03d4.png "g(x) = \sqrt[]{3} =====> g'(x) = 0")
![f'(x) = \frac{0 . x^{\frac{5}{2}} - \sqrt[]{3}.\frac{5}{2}.x^{\frac{3}{2}}}{(x^{\frac{5}{2}})^2}](/latexrender/pictures/220ab2fd2dfd6c5d8c0743c3aaac63d0.png "f'(x) = \frac{0 . x^{\frac{5}{2}} - \sqrt[]{3}.\frac{5}{2}.x^{\frac{3}{2}}}{(x^{\frac{5}{2}})^2}")
![f'(x) = - \frac{\sqrt[]{3}.\frac{5}{2}.x^{\frac{3}{2}}}{x^5}](/latexrender/pictures/accaacde70b7803734b9b9168dbc9b3f.png "f'(x) = - \frac{\sqrt[]{3}.\frac{5}{2}.x^{\frac{3}{2}}}{x^5}")
![f'(x) = - \sqrt[]{3} . \frac{5}{2} . x^{- \frac{7}{2}}](/latexrender/pictures/230822e601ad780e8d287be2238630a2.png "f'(x) = - \sqrt[]{3} . \frac{5}{2} . x^{- \frac{7}{2}}")
![f'(x) = \frac{- 5\sqrt[]{3}}{2}. \frac{1}{x^{\frac{7}{2}}}](/latexrender/pictures/a8c1f43a4b405ce3e2b1425211c3b893.png "f'(x) = \frac{- 5\sqrt[]{3}}{2}. \frac{1}{x^{\frac{7}{2}}}")
![f'(x) = \frac{- 5\sqrt[]{3}}{2\sqrt[]{x^7}}}](/latexrender/pictures/e852d912780e6b83febd94ef1d54d5fd.png "f'(x) = \frac{- 5\sqrt[]{3}}{2\sqrt[]{x^7}}}")
![\sqrt[]{3} * {x}^{-\frac{5}{2}}](/latexrender/pictures/69b4ba8659270963c7d7f3a5bdfeff87.png "\sqrt[]{3} * {x}^{-\frac{5}{2}}")
![\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}](/latexrender/pictures/981987c7bcdf9f8f498ca4605785636a.png "\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}")
![\sqrt[]{2}](/latexrender/pictures/f21662d1cabab6e8b273a4b6f1cd663a.png "\sqrt[]{2}")
e elevar ao quadrado os dois lados)