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![f(x)=6*tg^2(5x-1)\\\\\text{reescrevendo}\\\\f(x)=6*[tg(5x-1)]^2\\\\ \text{derivando}\\\\ f'(x)= 6*2*[tg(5x-1)]^{2-1} * [tg(5x-1)]'\\\\f'(x)=12*tg(5x-1)*[tg(5x-1)]'\\\\f'(x)=12*tg(5x-1)*sec^2(5x-1)*(5x-1)'\\\\f'(x)=12*tg(5x-1)*sec^2(5x-1)*(5-0)\\\\\boxed{\boxed{f'(x)= 60*tg(5x-1)*sec^2(5x-1)}}](https://tex.z-dn.net/?f=f%28x%29%3D6%2Atg%5E2%285x-1%29%5C%5C%5C%5C%5Ctext%7Breescrevendo%7D%5C%5C%5C%5Cf%28x%29%3D6%2A%5Btg%285x-1%29%5D%5E2%5C%5C%5C%5C+%5Ctext%7Bderivando%7D%5C%5C%5C%5C+f%27%28x%29%3D+6%2A2%2A%5Btg%285x-1%29%5D%5E%7B2-1%7D+%2A+%5Btg%285x-1%29%5D%27%5C%5C%5C%5Cf%27%28x%29%3D12%2Atg%285x-1%29%2A%5Btg%285x-1%29%5D%27%5C%5C%5C%5Cf%27%28x%29%3D12%2Atg%285x-1%29%2Asec%5E2%285x-1%29%2A%285x-1%29%27%5C%5C%5C%5Cf%27%28x%29%3D12%2Atg%285x-1%29%2Asec%5E2%285x-1%29%2A%285-0%29%5C%5C%5C%5C%5Cboxed%7B%5Cboxed%7Bf%27%28x%29%3D+60%2Atg%285x-1%29%2Asec%5E2%285x-1%29%7D%7D "f(x)=6*tg^2(5x-1)\\\\\text{reescrevendo}\\\\f(x)=6*[tg(5x-1)]^2\\\\ \text{derivando}\\\\ f'(x)= 6*2*[tg(5x-1)]^{2-1} * [tg(5x-1)]'\\\\f'(x)=12*tg(5x-1)*[tg(5x-1)]'\\\\f'(x)=12*tg(5x-1)*sec^2(5x-1)*(5x-1)'\\\\f'(x)=12*tg(5x-1)*sec^2(5x-1)*(5-0)\\\\\boxed{\boxed{f'(x)= 60*tg(5x-1)*sec^2(5x-1)}}")
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