WBJEE · Maths · Differentiation
Consider the non-constant differentiable function \(f\) of one variable which obeys the relation \(\frac{f(x)}{f(y)}=f(x-y) .\) If \(f^{\prime}(0)=p\) and \(f^{\prime}(5)=q,\) then \(f^{\prime}(-5)\) is
- A \(\frac{p^{2}}{q}\)
- B \(\frac{q}{p}\)
- C \(\frac{p}{q}\)
- D \(q\)
Answer & Solution
Correct Answer
(A) \(\frac{p^{2}}{q}\)
Step-by-step Solution
Detailed explanation
We have, \(\frac{f(x)}{f(y)}=f(x-y)\) \(\Rightarrow \quad f(x)=a^{k x}\) \(\therefore \quad f^{\prime}(x)=k a^{b x} \log a\) \(\begin{array}{lr}\text { Again, } & f^{\prime}(0)=P \\ \Rightarrow & k a^{\circ} \log a=P \\ \Rightarrow & k \log a=P\end{array}\) Also,…
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