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The functions f(x) f(x) and g(x) g(x) are differentiable. The function h(x) h(x) is defined as:\newlineh(x)=g(x)−f(x) h(x) = g(x) - f(x) \newlineIf f(2)=5 f(2) = 5 , f′(2)=−1 f'(2) = -1 , g(2)=−7 g(2) = -7 , and g′(2)=3 g'(2) = 3 , what is h′(2) h'(2) ?\newlineSimplify any fractions.\newlineh′(2)= h'(2) = ____

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Q. The functions f(x) f(x) and g(x) g(x) are differentiable. The function h(x) h(x) is defined as:\newlineh(x)=g(x)−f(x) h(x) = g(x) - f(x) \newlineIf f(2)=5 f(2) = 5 , f′(2)=−1 f'(2) = -1 , g(2)=−7 g(2) = -7 , and g′(2)=3 g'(2) = 3 , what is h′(2) h'(2) ?\newlineSimplify any fractions.\newlineh′(2)= h'(2) = ____
  1. Identify Derivative of h(x)h(x): Identify the derivative of h(x)h(x) using the properties of derivatives.\newlineSince h(x)=g(x)−f(x)h(x) = g(x) - f(x), by the linearity of the derivative, we have h′(x)=g′(x)−f′(x)h'(x) = g'(x) - f'(x).
  2. Substitute Values for h′(2)h'(2): Substitute the given values into the derivative of h(x)h(x) to find h′(2)h'(2). We have f′(2)=−1f'(2) = -1 and g′(2)=3g'(2) = 3, so h′(2)=g′(2)−f′(2)=3−(−1)=3+1h'(2) = g'(2) - f'(2) = 3 - (-1) = 3 + 1.
  3. Calculate h′(2)h'(2): Calculate the value of h′(2)h'(2).h′(2)=3+1=4h'(2) = 3 + 1 = 4.

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