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

Problem

d()/d(x)*5*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.

2. Apply the constant multiple rule to move the 5 outside of the derivative operator.

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

3. Recall the basic derivative rule for the natural logarithm function, which is d(ln(x))/d(x)=1/x

4. Substitute the derivative of the natural log back into the expression.

5⋅1/x

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

5/x

Final Answer

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

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