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If f(x)=(g(x))/(h(x)), then f^(')(1)= Submit Question

If f(x)=g(x)h(x) f(x)=\frac{g(x)}{h(x)} , then\newlinef′(1)= f^{\prime}(1)= \newlineSubmit Question

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Composition of linear and quadratic functions: find a valueright chevron icon

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Q. If f(x)=g(x)h(x) f(x)=\frac{g(x)}{h(x)} , then\newlinef′(1)= f^{\prime}(1)= \newlineSubmit Question
  1. Identify Rule: Identify the rule for differentiating a quotient, which is (fg)′=f′g−fg′g2(\frac{f}{g})' = \frac{f'g - fg'}{g^2}.
  2. Differentiate Functions: Differentiate g(x)g(x) and h(x)h(x) to find g′(x)g'(x) and h′(x)h'(x). Since we don't have explicit functions for g(x)g(x) and h(x)h(x), we represent their derivatives at x=1x=1 as g′(1)g'(1) and h′(1)h'(1).
  3. Apply Quotient Rule: Apply the quotient rule to find f′(x)=g′(x)h(x)−g(x)h′(x)(h(x))2f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2}.
  4. Substitute x=1x=1: Substitute x=1x=1 into the derivative to find f′(1)=g′(1)h(1)−g(1)h′(1)(h(1))2f'(1) = \frac{g'(1)h(1) - g(1)h'(1)}{(h(1))^2}.
  5. Further Calculation: Since we don't have the actual functions or their derivatives, we cannot calculate further without more information.

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