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

Problem

d()/d(x)*(log_2)(x)

Solution

1. Identify the function as a logarithm with a base other than e

2. Apply the change of base formula to rewrite the logarithm in terms of the natural logarithm, ln(x)

(log_2)(x)=ln(x)/ln(2)

3. Apply the constant multiple rule by treating 1/ln(2) as a constant coefficient.

d()/d(x)ln(x)/ln(2)=1/ln(2)d(ln(x))/d(x)

4. Differentiate the natural logarithm using the rule d(ln(x))/d(x)=1/x

1/ln(2)⋅1/x

5. Simplify the expression by multiplying the fractions.

1/(x*ln(2))

Final Answer

d()/d(x)*(log_2)(x)=1/(x*ln(2))

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