TS EAMCET · Maths · Differentiation
let \(g(x) \neq 0, g^{\prime}(x) \neq 0, f(x) \neq 0, f^{\prime}(x) \neq 0\). If \(F(x)=f(x) g(x), G(x)=f^{\prime}(x) g^{\prime}(x)\) and \(F^{\prime}(x)=G(x) H(x)=F(x) K(x)\), then \(H(x)+K(x)=\)
- A \(\frac{f^{\prime}}{f}+\frac{f}{f^{\prime}}+\frac{g}{g^{\prime}}\)
- B \(\frac{f^{\prime}}{f}+\frac{g}{g^{\prime}}+\frac{g^{\prime}}{g}\)
- C \(\frac{f^{\prime} g^{\prime}+f g}{f f^{\prime} g g^{\prime}}\)
- D \(\frac{f^{\prime}}{f}+\frac{g}{g^{\prime}}+\frac{f}{f^{\prime}}+\frac{g^{\prime}}{g}\)
Answer & Solution
Correct Answer
(D) \(\frac{f^{\prime}}{f}+\frac{g}{g^{\prime}}+\frac{f}{f^{\prime}}+\frac{g^{\prime}}{g}\)
Step-by-step Solution
Detailed explanation
We have, \(F(x)=f(x) g(x)\)…
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