Find the Derivative - d/dx log base 4 of x

Problem

d((log_4)(x))/d(x)

Solution

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

(log_4)(x)=ln(x)/ln(4)

2. Identify the constant factor in the expression to prepare for differentiation.

d((log_4)(x))/d(x)=d()/d(x)ln(x)/ln(4)

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

d((log_4)(x))/d(x)=1/ln(4)d(ln(x))/d(x)

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

d((log_4)(x))/d(x)=1/ln(4)⋅1/x

5. Simplify the expression by multiplying the fractions.

d((log_4)(x))/d(x)=1/(x*ln(4))

Final Answer

d((log_4)(x))/d(x)=1/(x*ln(4))

Want more problems? Check here!