Find the Derivative - d/dx natural log of x^8

Problem

d(ln(x8))/d(x)

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 which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x) where u=x8

3. Differentiate the inner function u=x8 using the Power Rule to get d(u)/d(x)=8*x7

4. Substitute these components into the Chain Rule formula.

d(ln(x8))/d(x)=1/(x8)⋅8*x7

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

(8*x7)/(x8)=8/x

Final Answer

d(ln(x8))/d(x)=8/x

Want more problems? Check here!