Find the Derivative - d/dx natural log of x^2+16

Problem

d(ln(x2+16))/d(x)

Solution

1. Identify the outer function as u=ln(v) and the inner function as v=x2+16

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

3. Differentiate the inner function x2+16 with respect to x which results in 2*x

4. Substitute the derivative of the inner function back into the chain rule formula.

5. Simplify the resulting expression by multiplying the terms.

Final Answer

d(ln(x2+16))/d(x)=(2*x)/(x2+16)

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