Find the Derivative - d/dx 2 log of x

Problem

d()/d(x)*2*(log_)(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 2 outside of the derivative.

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

3. Recall the derivative of the common logarithm (log_)(x) which is (log_10)(x) The derivative of (log_b)(x) is 1/(x*ln(b))

d((log_10)(x))/d(x)=1/(x*ln(10))

4. Multiply the constant 2 by the derivative of the logarithm.

2⋅1/(x*ln(10))=2/(x*ln(10))

Final Answer

d()/d(x)*2*(log_)(x)=2/(x*ln(10))

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