# Find the 2nd Derivative y=x natural log of x

Find the first derivative.
Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Differentiate using the Power Rule.
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Differentiate using the Power Rule which states that is where .
Multiply by .
Find the second derivative.
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 .
Find the third derivative.
Rewrite as .
Differentiate using the Power Rule which states that is where .
Rewrite the expression using the negative exponent rule .
Find the fourth derivative.
Differentiate using the Product Rule which states that is where and .
Differentiate.
Rewrite as .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Simplify the expression.
Multiply by .