Derivada
![y = \sqrt[4]{x}](https://tex.z-dn.net/?f=y+%3D++%5Csqrt%5B4%5D%7Bx%7D+ "y = \sqrt[4]{x}")
Soluções para a tarefa
Respondido por
1
Usando a seguinte regra
![y= \sqrt[n]{(x)} ~\to~y'= \frac{1}{n \sqrt[n]{x^{n-1}} }](https://tex.z-dn.net/?f=y%3D+%5Csqrt%5Bn%5D%7B%28x%29%7D+%7E%5Cto%7Ey%27%3D+%5Cfrac%7B1%7D%7Bn+%5Csqrt%5Bn%5D%7Bx%5E%7Bn-1%7D%7D+%7D+ "y= \sqrt[n]{(x)} ~\to~y'= \frac{1}{n \sqrt[n]{x^{n-1}} }")
aplicando
![\boxed{\boxed{y'= \frac{1}{4 \sqrt[4]{x^3} } }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7By%27%3D+%5Cfrac%7B1%7D%7B4+%5Csqrt%5B4%5D%7Bx%5E3%7D+%7D+%7D%7D "\boxed{\boxed{y'= \frac{1}{4 \sqrt[4]{x^3} } }}")
modo tradicional
![y= \sqrt[4]{x} \\ \\y=x^{ \frac{1}{4} }\\ \\y'= \frac{1}{4} *x^{- \frac{3}{4} }](https://tex.z-dn.net/?f=y%3D+%5Csqrt%5B4%5D%7Bx%7D+%5C%5C+%5C%5Cy%3Dx%5E%7B+%5Cfrac%7B1%7D%7B4%7D+%7D%5C%5C+%5C%5Cy%27%3D+%5Cfrac%7B1%7D%7B4%7D+%2Ax%5E%7B-+%5Cfrac%7B3%7D%7B4%7D+%7D "y= \sqrt[4]{x} \\ \\y=x^{ \frac{1}{4} }\\ \\y'= \frac{1}{4} *x^{- \frac{3}{4} }")
![\boxed{\boxed{y'= \frac{1}{ 4\sqrt[4]{x^3} }}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7By%27%3D+%5Cfrac%7B1%7D%7B+4%5Csqrt%5B4%5D%7Bx%5E3%7D+%7D%7D%7D "\boxed{\boxed{y'= \frac{1}{ 4\sqrt[4]{x^3} }}}")
aplicando
modo tradicional
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