Find the Derivative - d/dx y = natural log of x^6

Problem

d()/d(x)*ln(x6)

Solution

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

2. Identify the inner function as u=x6 and its derivative as d(x6)/d(x)=6*x5

3. Substitute these into the chain rule formula to get 1/(x6)⋅6*x5

4. Simplify the resulting expression by canceling the common factors of x

Final Answer

d(ln(x6))/d(x)=6/x

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