WBJEE · Maths · Differentiation
Let \(F(x)=e^{x}, G(x)=e^{-x}\) and \(H(x)=G(F(x)),\) where \(x\) is a real variable. Then, \(\frac{d H}{d x}\) at \(x=0\) is
- A 1
- B -1
- C \(-\frac{1}{e}\)
- D \(-e\)
Answer & Solution
Correct Answer
(C) \(-\frac{1}{e}\)
Step-by-step Solution
Detailed explanation
We have, \(F(x)=e^{x}, G(x)=e^{-x}\) \(\therefore \quad H(x)=G(F(x))\) \(\begin{aligned} &=G\left(e^{x}\right) \\ &=e^{-e^{x}} \\ \frac{d H}{d x} &=e^{-e^{x}} \cdot\left(-e^{x}\right) \\ &=-e^{x} e^{-e^{x}} \end{aligned}\)…
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