Find the Derivative - d/dx y = natural log of x^5

Problem

d()/d(x)*ln(x5)

Solution

1. Identify the function as a composition of the natural logarithm and a power 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. Substitute u=x5 into the chain rule formula.

4. Differentiate the inner function x5 using the power rule to get 5*x4

5. Multiply the results together to get 1/(x5)⋅5*x4

6. Simplify the expression by canceling the common factors of x

Final Answer

d(ln(x5))/d(x)=5/x

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