Find the Derivative - d/dt t natural log of t

Problem

d()/d(t)*t*ln(t)

Solution

1. Identify the rule needed for the expression t*ln(t) which is the product of two functions of t

2. Apply the product rule, which states that d()/d(t)*[ƒ(t)*g(t)]=ƒ(t)d(g(t))/d(t)+g(t)d(ƒ(t))/d(t)

3. Set ƒ(t)=t and g(t)=ln(t)

4. Differentiate each part: d(t)/d(t)=1 and d(ln(t))/d(t)=1/t

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

t⋅1/t+ln(t)⋅1

6. Simplify the expression by canceling t in the first term.

1+ln(t)

Final Answer

d()/d(t)*t*ln(t)=1+ln(t)

Want more problems? Check here!