Find the Derivative - d/dx natural log of 4x+7

Problem

d(ln(4*x+7))/d(x)

Solution

1. Identify the outer function as ln(u) and the inner function as u=4*x+7

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

3. Differentiate the inner function 4*x+7 with respect to x to find d(u)/d(x)=4

4. Substitute the expressions back into the chain rule formula.

5. Simplify the resulting fraction.

Final Answer

d(ln(4*x+7))/d(x)=4/(4*x+7)

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