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f-5-x-4-sin-x-f-7-x-

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Question Number 83782 by jagoll last updated on 06/Mar/20
f^((5)) (x) = 4^(−sin x) f^((7)) (x) =?
f(5)(x)=4−sinxf(7)(x)=?
Commented by john santu last updated on 06/Mar/20
f^((n)) (x) = [ f^((n−1)) (x) ]′ f^((6)) (x) = [ f^((5)) (x)] ′ = −cos x. 4^(−sin x) . ln (4) f^((7)) (x)= ln(4) [ sin x. 4^(−sin x) +ln(4) cos^2 x.4^(−sin x) ]
f(n)(x)=[f(n−1)(x)]′f(6)(x)=[f(5)(x)]′=−cosx.4−sinx.ln(4)f(7)(x)=ln(4)[sinx.4−sinx+ln(4)cos2x.4−sinx]

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