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

Differentiate using the Quotient Rule which states that is where and .
The derivative of with respect to is .
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Combine and .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply by .
Use the quotient property of logarithms, .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Rewrite as a product.
Multiply and .
Simplify.
Simplify the numerator.
Logarithm base of is .