Question

find (\frac{d^2 y}{dx^2}). (y = 3x - 4) (\frac{d^2 y}{dx^2} = square)

Explanation:

Step1: Find the first derivative

To find the first derivative \(\frac{dy}{dx}\) of \(y = 3x - 4\), we use the power rule. The derivative of \(ax^n\) is \(nax^{n - 1}\). For \(y = 3x - 4\), the derivative of \(3x\) is \(3\) (since \(n = 1\), so \(1\times3x^{1 - 1}=3\)) and the derivative of the constant \(-4\) is \(0\). So, \(\frac{dy}{dx}=3\).

Step2: Find the second derivative

Now, we find the second derivative \(\frac{d^2y}{dx^2}\) by differentiating \(\frac{dy}{dx}\). The derivative of the constant \(3\) is \(0\) (because the derivative of a constant \(c\) is \(0\), i.e., if \(f(x)=c\), then \(f^\prime(x) = 0\)). So, \(\frac{d^2y}{dx^2}=0\).

Answer:

\(0\)