Find the Derivative - d/dx y=2 natural log of x

Problem

d()/d(x)*(2*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 the function.

2. Apply the constant multiple rule to move the coefficient 2 outside of the derivative operation.

(d(2)*ln(x))/d(x)=2d(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 ln(x) back into the expression.

2⋅1/x

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

2/x

Final Answer

(d(2)*ln(x))/d(x)=2/x

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