TS EAMCET · Maths · Differentiation
If \(f(x)=\frac{e^{2 x}-e^{-2 x}}{e^{3 x}+e^{-3 x}}\), then \(f^{\prime}(0)=\)
- A \(-1\)
- B \(0\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} f(x) & =\frac{e^{2 x}-e^{-2 x}}{e^{3 x}+e^{-3 x}} \\ \Rightarrow f^{\prime}(x) & =\frac{\left(e^{3 x}+e^{-3 x}\right)\left(2 e^{2 x}+2 e^{-2 x}\right)}{\left(e^{2 x}-e^{-2 x}\right)\left(3 e^{3 x}-3 e^{-3 x}\right)} \\ \Rightarrow f^{\prime}(0) & =\frac{(1+1)(2…
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