Chapter 4.4, Problem 28E

To determine

To calculate: The derivative of y with respect to x .

Answer to Problem 28E

The derivative is $\frac{dy}{dx}=\ln \left(10\right)$ .

Explanation of Solution

Given information: The equation of y in terms of x is given as,

  $y=\ln \left({10}^x\right)$

Formula Used: $\frac{d\left(x^n\right)}{dx}=n\times x^{\left(n-1\right)}$

Calculation: Using the derivation,

  $\begin{array}{l}y=\ln \left({10}^x\right)\\ y=x\times \ln \left(10\right)\\ \frac{dy}{dx}=\frac{d\left(x\times \ln \left(10\right)\right)}{dx}\\ \frac{dy}{dx}=\ln \left(10\right)\end{array}$

So the derivative is $\frac{dy}{dx}=\ln \left(10\right)$ .