Derive a função: (1/21)(3x-2)^7
(REGRA DE CADEIA)
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A Regra da Cadeia é usada para derivar funções compostas.
Dada a seguinte função
podemos enxergá-la como
Derivando
pela Regra da Cadeia, temos
![f'(x)=\left[\dfrac{1}{21}\,(g(x))^7 \right ]'\\\\\\ f'(x)=\dfrac{1}{21}\left[(g(x))^7 \right ]'\\\\\\ f'(x)=\dfrac{1}{21}\cdot 7\,(g(x))^{7-1}\cdot g'(x)\\\\\\ f'(x)=\dfrac{7}{21}\,(g(x))^{6}\cdot g'(x)\\\\\\ f'(x)=\dfrac{1}{3}\,(3x-2)^{6}\cdot (3x-2)'\\\\\\ f'(x)=\dfrac{1}{3}\,(3x-2)^{6}\cdot 3\\\\\\ \therefore~~\boxed{\begin{array}{c}f'(x)=(3x-2)^{6} \end{array}}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cleft%5B%5Cdfrac%7B1%7D%7B21%7D%5C%2C%28g%28x%29%29%5E7+%5Cright+%5D%27%5C%5C%5C%5C%5C%5C+f%27%28x%29%3D%5Cdfrac%7B1%7D%7B21%7D%5Cleft%5B%28g%28x%29%29%5E7+%5Cright+%5D%27%5C%5C%5C%5C%5C%5C+f%27%28x%29%3D%5Cdfrac%7B1%7D%7B21%7D%5Ccdot+7%5C%2C%28g%28x%29%29%5E%7B7-1%7D%5Ccdot+g%27%28x%29%5C%5C%5C%5C%5C%5C+f%27%28x%29%3D%5Cdfrac%7B7%7D%7B21%7D%5C%2C%28g%28x%29%29%5E%7B6%7D%5Ccdot+g%27%28x%29%5C%5C%5C%5C%5C%5C+f%27%28x%29%3D%5Cdfrac%7B1%7D%7B3%7D%5C%2C%283x-2%29%5E%7B6%7D%5Ccdot+%283x-2%29%27%5C%5C%5C%5C%5C%5C+f%27%28x%29%3D%5Cdfrac%7B1%7D%7B3%7D%5C%2C%283x-2%29%5E%7B6%7D%5Ccdot+3%5C%5C%5C%5C%5C%5C+%5Ctherefore%7E%7E%5Cboxed%7B%5Cbegin%7Barray%7D%7Bc%7Df%27%28x%29%3D%283x-2%29%5E%7B6%7D+%5Cend%7Barray%7D%7D "f'(x)=\left[\dfrac{1}{21}\,(g(x))^7 \right ]'\\\\\\ f'(x)=\dfrac{1}{21}\left[(g(x))^7 \right ]'\\\\\\ f'(x)=\dfrac{1}{21}\cdot 7\,(g(x))^{7-1}\cdot g'(x)\\\\\\ f'(x)=\dfrac{7}{21}\,(g(x))^{6}\cdot g'(x)\\\\\\ f'(x)=\dfrac{1}{3}\,(3x-2)^{6}\cdot (3x-2)'\\\\\\ f'(x)=\dfrac{1}{3}\,(3x-2)^{6}\cdot 3\\\\\\ \therefore~~\boxed{\begin{array}{c}f'(x)=(3x-2)^{6} \end{array}}")
Dada a seguinte função
podemos enxergá-la como
Derivando
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