DERIVADA
f(x)=ln(x^2-6x+8)
poderiam me mostrar passo a passo por favor!
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DERIVADA
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Para derivarmos a função em relação a x, vamos utilizar a Regra da Cadeia:
Dessa forma:
![f(x)=\ln(x^2-6x+8)\\\\
f'(x)=\dfrac{d}{dx}[\ln(x^2-6x+8)]\\\\
f'(x)=[\ln(x^2-6x+8)]'\cdot(x^2-6x+8)'\\\\
f'(x)=\dfrac{1}{x^2-6x+8}\cdot(2x-6)\\\\
f'(x)=\dfrac{2x-6}{x^2-6x+8}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cln%28x%5E2-6x%2B8%29%5C%5C%5C%5C%0Af%27%28x%29%3D%5Cdfrac%7Bd%7D%7Bdx%7D%5B%5Cln%28x%5E2-6x%2B8%29%5D%5C%5C%5C%5C%0Af%27%28x%29%3D%5B%5Cln%28x%5E2-6x%2B8%29%5D%27%5Ccdot%28x%5E2-6x%2B8%29%27%5C%5C%5C%5C%0Af%27%28x%29%3D%5Cdfrac%7B1%7D%7Bx%5E2-6x%2B8%7D%5Ccdot%282x-6%29%5C%5C%5C%5C%0Af%27%28x%29%3D%5Cdfrac%7B2x-6%7D%7Bx%5E2-6x%2B8%7D "f(x)=\ln(x^2-6x+8)\\\\
f'(x)=\dfrac{d}{dx}[\ln(x^2-6x+8)]\\\\
f'(x)=[\ln(x^2-6x+8)]'\cdot(x^2-6x+8)'\\\\
f'(x)=\dfrac{1}{x^2-6x+8}\cdot(2x-6)\\\\
f'(x)=\dfrac{2x-6}{x^2-6x+8}")
Dessa forma:
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