Find the Derivative - d/dx y = log of 10x

Problem

d()/d(x)*ln(10*x)

Solution

1. Identify the function as a composition of the natural logarithm and a linear function, u=10*x

2. Apply the chain rule, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Differentiate the inner function 10*x with respect to x which results in 10

4. Substitute these values into the chain rule formula:

d(ln(10*x))/d(x)=1/(10*x)⋅10

5. Simplify the expression by canceling the constant factor 10 from the numerator and denominator.

10/(10*x)=1/x

Final Answer

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

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