Find the Derivative - d/dx log of x^2

Problem

d((log_)(x2))/d(x)

Solution

1. Identify the function as a common logarithm (base 10) and apply the change of base formula to rewrite it in terms of the natural logarithm.

(log_)(x2)=ln(x2)/ln(10)

2. Apply the power rule for logarithms to simplify the expression before differentiating.

ln(x2)/ln(10)=(2*ln(x))/ln(10)

3. Differentiate the expression using the constant multiple rule and the derivative of the natural logarithm, where d(ln(x))/d(x)=1/x

d()/d(x)(2*ln(x))/ln(10)=2/ln(10)⋅1/x

4. Simplify the resulting expression into a single fraction.

2/(x*ln(10))

Final Answer

d((log_)(x2))/d(x)=2/(x*ln(10))

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