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derivative od e^-x^2

derivative od e^-x^2

Grade:11

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
f(x) = e^{-x^{2}}
f'(x) = e^{-x^{2}}.(-2x)
f'(x) = -2x.e^{-x^{2}}
f'(x) = \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}
f'(x) = \lim_{h\rightarrow 0}\frac{e^{-(x+h)^{2}}-e^{-x^{2}}}{h}
f'(x) = \lim_{h\rightarrow 0}e^{-x^{2}}.\frac{e^{-(h^{2}+2hx)}-1}{h}
f'(x) = \lim_{h\rightarrow 0}e^{-x^{2}}.\frac{e^{-(h^{2}+2hx)}-1}{h}.\frac{-(h^{2}+2hx)}{-(h^{2}+2hx)}
f'(x) = \lim_{h\rightarrow 0}e^{-x^{2}}.\frac{e^{-(h^{2}+2hx)}-1}{-(h^{2}+2hx)}.\frac{-(h^{2}+2hx)}{h}
\lim_{h\rightarrow 0}\frac{e^{-(h^{2}+2hx)}-1}{-(h^{2}+2hx)} = 1
f'(x) = \lim_{h\rightarrow 0}e^{-x^{2}}.-(h+2x)
f'(x) = -2xe^{-x^{2}}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
moidin afsan
20 Points
8 years ago
thank u very much

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