Find the Derivative - d/dx natural log of 2x+1

Problem

d(ln(2*x+1))/d(x)

Solution

1. Identify the outer function as ƒ(u)=ln(u) and the inner function as u=2*x+1

2. Apply the chain rule, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Differentiate the inner function u=2*x+1 with respect to x

d(2*x+1)/d(x)=2

4. Substitute the inner function and its derivative into the chain rule formula.

d(ln(2*x+1))/d(x)=1/(2*x+1)⋅2

5. Simplify the resulting expression by multiplying the terms.

2/(2*x+1)

Final Answer

d(ln(2*x+1))/d(x)=2/(2*x+1)

Want more problems? Check here!