Question

the following table lists the values of functions f and h, and of their derivatives, f and h, for x = -1. evaluate \\( \frac { d } { d x } f ( x ) \cdot h ( x ) \\) at x = -1.

Explanation:

Step1: Apply the product rule

The product rule states that \((uv)^\prime = u^\prime v+uv^\prime\). Let \(u = f(x)\) and \(v = h(x)\). Then \(\frac{d}{dx}[f(x)\cdot h(x)]=f^\prime(x)h(x)+f(x)h^\prime(x)\)

Step2: Substitute \(x = - 1\)

When \(x=-1\), we substitute \(f(-1)=-3\), \(h(-1)=-4\), \(f^\prime(-1) = 1\), and \(h^\prime(-1)=3\) into the formula \(f^\prime(x)h(x)+f(x)h^\prime(x)\)

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Answer:

\(-13\)