Function

Let f(x+y)=f(x).f(y) and f(x)=1+sin(3x).g(x) where g(x) is cont. , then f'(x) is

a) f(x).g(0)
b)3g(0)
c) f(x).cos(3x)
d)3f(x).g(0)
e)3f(x).g(x)

2 Answers

1133

Sourish Ghosh ·2013-12-22 21:42:28

1133

Sourish Ghosh ·2013-12-23 23:16:58

f'(x) = lim (h->0) f(x+h) - f(x)h
= f(x)f(h) - f(x)h
=f(x)[f(h) - 1]h
=f(x)[sin(3h)g(h)]h
=f(x)[sin(3h)g(h)]3hx3
=3f(x)g(h)
=3f(x)g(0)

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