Olá,
Estou com dúvida em uma derivada simples, precisava do passo-a-passo
1) Derivada de √(6x-5)
Soluções para a tarefa
Respondido por
0
Preparando a função:
Resolvendo a derivada pela regra da cadeia, que é a deriva de fora vezes derivada de dentro:
![f'_{(x)}=[(6x-5)^{\frac{1}{2}}]'\times(6x-5)'\\\\\\ f'_{(x)}=\dfrac{1}{2}(6x-5)^{(\frac{1}{2}-1)}\times(6x^{1-1}-0)\\\\\\ f'_{(x)}=\dfrac{1}{2}(6x-5)^{-\frac{1}{2}}\times(6x^{0}-0)\\\\\\ f'_{(x)}=\dfrac{1}{2}(6x-5)^{-\frac{1}{2}}\times6\\\\\\ f'_{(x)}=\dfrac{6}{2}(6x-5)^{-\frac{1}{2}}\\\\\\ f'_{(x)}=\dfrac{6}{2}\dfrac{1}{(6x-5)^{\frac{1}{2}}}\\\\\\ f'_{(x)}=\dfrac{6}{2}\dfrac{1}{\sqrt{6x-5}}\\\\\\ f'_{(x)}=\dfrac{6}{2\sqrt{6x-5}}\ (simplificando)\\\\\\ \boxed{f'_{(x)}=\dfrac{3}{\sqrt{6x-5}}}](https://tex.z-dn.net/?f=f%27_%7B%28x%29%7D%3D%5B%286x-5%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D%27%5Ctimes%286x-5%29%27%5C%5C%5C%5C%5C%5C+f%27_%7B%28x%29%7D%3D%5Cdfrac%7B1%7D%7B2%7D%286x-5%29%5E%7B%28%5Cfrac%7B1%7D%7B2%7D-1%29%7D%5Ctimes%286x%5E%7B1-1%7D-0%29%5C%5C%5C%5C%5C%5C+f%27_%7B%28x%29%7D%3D%5Cdfrac%7B1%7D%7B2%7D%286x-5%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Ctimes%286x%5E%7B0%7D-0%29%5C%5C%5C%5C%5C%5C+f%27_%7B%28x%29%7D%3D%5Cdfrac%7B1%7D%7B2%7D%286x-5%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5Ctimes6%5C%5C%5C%5C%5C%5C+f%27_%7B%28x%29%7D%3D%5Cdfrac%7B6%7D%7B2%7D%286x-5%29%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C+f%27_%7B%28x%29%7D%3D%5Cdfrac%7B6%7D%7B2%7D%5Cdfrac%7B1%7D%7B%286x-5%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%5C%5C%5C%5C%5C%5C+f%27_%7B%28x%29%7D%3D%5Cdfrac%7B6%7D%7B2%7D%5Cdfrac%7B1%7D%7B%5Csqrt%7B6x-5%7D%7D%5C%5C%5C%5C%5C%5C+f%27_%7B%28x%29%7D%3D%5Cdfrac%7B6%7D%7B2%5Csqrt%7B6x-5%7D%7D%5C+%28simplificando%29%5C%5C%5C%5C%5C%5C+%5Cboxed%7Bf%27_%7B%28x%29%7D%3D%5Cdfrac%7B3%7D%7B%5Csqrt%7B6x-5%7D%7D%7D "f'_{(x)}=[(6x-5)^{\frac{1}{2}}]'\times(6x-5)'\\\\\\ f'_{(x)}=\dfrac{1}{2}(6x-5)^{(\frac{1}{2}-1)}\times(6x^{1-1}-0)\\\\\\ f'_{(x)}=\dfrac{1}{2}(6x-5)^{-\frac{1}{2}}\times(6x^{0}-0)\\\\\\ f'_{(x)}=\dfrac{1}{2}(6x-5)^{-\frac{1}{2}}\times6\\\\\\ f'_{(x)}=\dfrac{6}{2}(6x-5)^{-\frac{1}{2}}\\\\\\ f'_{(x)}=\dfrac{6}{2}\dfrac{1}{(6x-5)^{\frac{1}{2}}}\\\\\\ f'_{(x)}=\dfrac{6}{2}\dfrac{1}{\sqrt{6x-5}}\\\\\\ f'_{(x)}=\dfrac{6}{2\sqrt{6x-5}}\ (simplificando)\\\\\\ \boxed{f'_{(x)}=\dfrac{3}{\sqrt{6x-5}}}")
Espero ter ajudado.
Bons estudos!
Resolvendo a derivada pela regra da cadeia, que é a deriva de fora vezes derivada de dentro:
Espero ter ajudado.
Bons estudos!
paulinhacamargo1:
Obrigada pela explicação! :)
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