Posted by Subhotosh Khan on August 12, 2002 at 09:27:31:
In Reply to: y=3^x posted by bana on August 12, 2002 at 07:53:27:
: Hi thre,
: I've been told that if y=3^x, then y'=(In3)3^x . how does it work with the rule In{g(x)}-> g'/g?
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First of all"
y = 3^x
y' = 3^x * ln 3(...not "In")
To prove that:
y = 3^x
ln y = x * ln 3 (... taking 'ln' of both sides)
y'/y = ln 3 (...differentiating both sides)
y' = y * ln 3 = 3^x * ln 3