Apply the quotient rule, which is:
dxdg(x)f(x)=g2(x)−f(x)dxdg(x)+g(x)dxdf(x)
f(x)=log(x)2 and g(x)=x.
To find dxdf(x):
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Let u=log(x).
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Apply the power rule: u2 goes to 2u
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Then, apply the chain rule. Multiply by dxdlog(x):
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The derivative of log(x) is x1.
The result of the chain rule is:
x2log(x)
To find dxdg(x):
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Apply the power rule: x goes to 1
Now plug in to the quotient rule:
x2−log(x)2+2log(x)