Find the Derivative - d/dx 9 natural log of x

Problem

d()/d(x)*9*ln(x)

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of that function.

d()/d(x)*9*ln(x)=9d(ln(x))/d(x)

2. Apply the derivative rule for the natural logarithm function, which is d(ln(x))/d(x)=1/x

9d(ln(x))/d(x)=9⋅1/x

3. Simplify the expression by multiplying the constant and the fraction.

9⋅1/x=9/x

Final Answer

d()/d(x)*9*ln(x)=9/x

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