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Differentiate following functions.
(a) R ( w) = 4^{w} - 5 log_{9} w
(b) f ( x ) = 3e^{x} + 10x^{3} ln x
Solution : (a) It will be the only example which doesn't includes the natural exponential & natural logarithm functions.
R′ ( w) = 4^{w} ln 4 - (5/w ln 9)
(b) Not much to this one. Just recall using the product rule on the second term.
f ′ ( x ) = 3e^{x} + 30x^{2} ln x + 10x^{3} ( 1 /x)
= 3e^{x} +30x^{2} ln x + 10x^{2}
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