Find the Derivative - d/dx natural log of 6-5x

Problem

d(ln(6−5*x))/d(x)

Solution

1. Identify the function as a natural logarithm of a composite function, which requires the use of the chain rule.

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

3. Define the inner function as u=6−5*x

4. Differentiate the inner function to find d(u)/d(x)=−5

5. Substitute these values into the chain rule formula to get 1/(6−5*x)⋅(−5)

6. Simplify the expression by multiplying the terms.

Final Answer

d(ln(6−5*x))/d(x)=−5/(6−5*x)

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