Find the Derivative – d/dx y=( log of x)/(1+ log of x)

Math
Differentiate using the Quotient Rule which states that is where and .
The derivative of with respect to is .
Differentiate.
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By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Add and .
The derivative of with respect to is .
Combine and .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Combine and .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply by .
Use the quotient property of logarithms, .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Rewrite as a product.
Multiply and .
Simplify.
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Simplify the numerator.
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Logarithm base of is .
Add and .
Reorder terms.
Find the Derivative – d/dx y=( log of x)/(1+ log of x)

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