Find the Derivative - d/dx x^3 natural log of x

Problem

d()/d(x)*x3*ln(x)

Solution

1. Identify the rule needed for the expression x3*ln(x) which is the product of two functions u=x3 and v=ln(x)

2. Apply the product rule formula, which states (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the individual components: d(x3)/d(x)=3*x2 and d(ln(x))/d(x)=1/x

4. Substitute these derivatives back into the product rule formula:

x3⋅1/x+ln(x)⋅3*x2

5. Simplify the first term by dividing x3 by x

x2+3*x2*ln(x)

6. Factor out the common term x2 to reach the final form:

x2*(1+3*ln(x))

Final Answer

(d(x3)*ln(x))/d(x)=x2*(1+3*ln(x))

Want more problems? Check here!