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

Problem

d((log_2)(x))/d(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 expression in terms of the natural logarithm, where (log_b)(x)=ln(x)/ln(b)

3. Rewrite the expression as a constant multiple of the natural logarithm.

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

4. Apply the constant multiple rule by pulling the constant 1/ln(2) outside of the derivative.

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

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

d((log_2)(x))/d(x)=1/ln(2)⋅1/x

6. Simplify the resulting expression into a single fraction.

Final Answer

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

Want more problems? Check here!