Find the Derivative - d/dx natural log of x^3-7

Problem

d(ln(x3−7))/d(x)

Solution

1. Identify the outer function as u=ln(g(x)) and the inner function as g(x)=x3−7

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

3. Differentiate the inner function x3−7 with respect to x using the power rule to get 3*x2

4. Substitute the components into the chain rule formula to get 1/(x3−7)⋅3*x2

5. Simplify the expression by multiplying the terms.

Final Answer

d(ln(x3−7))/d(x)=(3*x2)/(x3−7)

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