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how to differentiate 2^sinx by taking logarithm pls explain with full soln

how to differentiate 2^sinx by taking logarithm pls explain with full soln

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
L = 2^sinx.....(1)
Take logarithm with base 2 on both sides
log2L = log2(2^sinx)
log2L = sinx
Differentiate both sides w.r.t x; we have
(1/L) dL/dx = cosx
dL/dx = L.cosx
Put L from (1)
dL/dx = (2^sinx).cosx
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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