Questions: Find the first and second derivatives. y=3x+6 dy/dx=3 d^2y/dx^2=

Transcript text: Find the first and second derivatives. \[ y=3 x+6 \] \[ \begin{array}{l} \frac{d y}{d x}=3 \\ \frac{d^{2} y}{d x^{2}}= \end{array} \]

Solution

Solution Steps

To find the first and second derivatives of the function \( y = 3x + 6 \), we will use basic differentiation rules. The first derivative of a linear function \( ax + b \) is simply the coefficient \( a \). The second derivative of a constant or linear function is zero.

Step 1: Identify the Function

The given function is \( y = 3x + 6 \).

Step 2: Calculate the First Derivative

To find the first derivative of \( y \) with respect to \( x \), we differentiate the function: \[ \frac{dy}{dx} = \frac{d}{dx}(3x + 6) = 3 \]

Step 3: Calculate the Second Derivative

To find the second derivative, we differentiate the first derivative: \[ \frac{d^2y}{dx^2} = \frac{d}{dx}(3) = 0 \]