Find the Derivative - d/dx log of 7x

Problem

d((log_)(7*x))/d(x)

Solution

1. Identify the function as a common logarithm, which is assumed to be base 10, written as (log_10)(7*x)

2. Apply the change of base formula to rewrite the expression in terms of the natural logarithm.

(log_10)(7*x)=ln(7*x)/ln(10)

3. Apply the chain rule and the derivative rule for natural logarithms, where d(ln(u))/d(x)=1/u⋅d(u)/d(x)

d()/d(x)ln(7*x)/ln(10)=1/ln(10)⋅1/(7*x)⋅(d(7)*x)/d(x)

4. Differentiate the inner function 7*x which results in 7

1/ln(10)⋅1/(7*x)⋅7

5. Simplify the expression by canceling the constant factor 7 in the numerator and denominator.

1/(x*ln(10))

Final Answer

d((log_)(7*x))/d(x)=1/(x*ln(10))

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