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Question Number 83782 by jagoll last updated on 06/Mar/20

$${\mathrm{f}}^{\left(5\right)}\left(\mathrm{x}\right)=4^{-\sin \mathrm{x}}$$$${\mathrm{f}}^{\left(7\right)}\left(\mathrm{x}\right)=?$$

Commented by john santu last updated on 06/Mar/20

$${\mathrm{f}}^{\left(\mathrm{n}\right)}\left(x\right)={\left[{\mathrm{f}}^{(\mathrm{n}-1)}\left(x\right)\right]}^{\prime }$$$${\mathrm{f}}^{\left(6\right)}\left(x\right)=\left[{\mathrm{f}}^{\left(5\right)}\left(x\right)\right]{}^{\prime }=-\cos x.4^{-\sin x}.\ln \left(4\right)$$$${\mathrm{f}}^{\left(7\right)}\left(x\right)=\ln \left(4\right)[\sin x.4^{-\sin x}+\ln \left(4\right)\cos {}^{2}x.4^{-\sin x}]$$

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