# Find the Derivative – d/dx y = square root of x natural log of x

Rewrite as .
Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Combine fractions.
Combine and .
Move to the denominator using the negative exponent rule .
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
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.
Simplify the numerator.
Multiply by .
Subtract from .
Differentiate using the Power Rule which states that is where .
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.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Combine and .
Combine and .
Move to the denominator using the negative exponent rule .
Find the Derivative – d/dx y = square root of x natural log of x