Differentiate using the Quotient Rule which states that is where and .

The derivative of with respect to is .

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 .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Combine and .

Combine and .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor.

Divide by .

Multiply by .

Use the quotient property of logarithms, .

Cancel the common factor.

Divide by .

Rewrite as a product.

Multiply and .

Simplify the numerator.

Logarithm base of is .

Add and .

Reorder terms.

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