Find the Derivative - d/d@VAR f(x)=2x^3 natural log of x

Problem

d()/d(x)*(2*x3*ln(x))

Solution

1. Identify the function as a product of two terms, u=2*x3 and v=ln(x) which requires the product rule.

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

3. Differentiate the first term u=2*x3 using the power rule to get (d(2)*x3)/d(x)=6*x2

4. Differentiate the second term v=ln(x) to get d(ln(x))/d(x)=1/x

5. Substitute these derivatives back into the product rule formula.

2*x3⋅1/x+ln(x)⋅6*x2

6. Simplify the expression by multiplying the terms.

2*x2+6*x2*ln(x)

7. Factor out the common term 2*x2 to reach the final form.

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

Final Answer

(d(2)*x3*ln(x))/d(x)=2*x2*(1+3*ln(x))

Want more problems? Check here!