Question

In Exercises \(1-28\) , find \(d y / d x\) . Remember that you can use NDER to support your computations. $$y=\ln 2 \cdot \log _{2} x$$

Short answer

The derivative of the function \( y = \ln 2 \cdot \log_2 x \) is \( \frac{d y}{d x} = \frac{1}{x} \)

Step-by-step solution

Identify the function and its derivative

First, recognize the function inside the logarithm, which is \(x\) in this case. Therefore, \(f(x) = x\) and its derivative \(f'(x)\) is \(1\).

Apply the differentiation formula

Apply the differentiation formula to the function. This gives us \( \frac{d}{dx} \log_2 x = \frac{1}{x \ln 2} \cdot 1\).

Final Simplification

Finally, simplify the derivative to its simplest form which gives it as: \( \frac{d y}{d x} = \frac{\ln 2}{x \ln 2} = \frac{1}{x} \)