Questions: Find the derivative of y=19^x

Transcript text: Find the derivative of $y=19^{x}$

Solution

Solution Steps

To find the derivative of the function $ y = 19^x $, we can use the property of exponential functions. The derivative of $ a^x $ with respect to $ x $ is $ a^x \ln(a) $. Therefore, we apply this rule to find the derivative of $ 19^x $.

Step 1: Define the Function

We start with the function given by $ y = 19^x $.

Step 2: Apply the Derivative Rule

To find the derivative of $ y $ with respect to $ x $, we use the rule for the derivative of an exponential function. The derivative of $ a^x $ is given by: \[ \frac{dy}{dx} = a^x \ln(a) \] In our case, $ a = 19 $. Therefore, we have: \[ \frac{dy}{dx} = 19^x \ln(19) \]

Step 3: Write the Final Derivative

Thus, the derivative of the function $ y = 19^x $ is: \[ \frac{dy}{dx} = 19^x \ln(19) \]