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Question Number 112874 by sandy_delta last updated on 10/Sep/20

$$\mathrm{y}=\sec \left\{\sec \left[\tan \left(\tan \left(\sin {4\mathrm{x}}^2\right)\right)\right]\right\}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=?$$

Commented by MJS_new last updated on 10/Sep/20

$$f_1\left(f_2\left(f_3\left(f_4\left(f_5\left(f_6\left(x\right)\right)\right)\right)\right)\right)=$$$$=f_1^{\prime }\left(f_2\left(f_3\left(f_4\left(f_5\left(f_6\left(x\right)\right)\right)\right)\right)\right)\times$$$$\times f_2^{\prime }\left(f_3\left(f_4\left(f_5\left(f_6\left(x\right)\right)\right)\right)\right)\times$$$$\times f_3^{\prime }\left(f_4\left(f_5\left(f_6\left(x\right)\right)\right)\right)\times$$$$\times f_4^{\prime }\left(f_5\left(f_6\left(x\right)\right)\right)\times$$$$\times f_5^{\prime }\left(f_6\left(x\right)\right)\times$$$$\times f_6^{\prime }\left(x\right)$$

Commented by sandy_delta last updated on 10/Sep/20

$$\mathrm{thanks}\mathrm{very}\mathrm{much}\mathrm{Sir}$$

Answered by bobhans last updated on 10/Sep/20

$$8\mathrm{xcos}\left({4\mathrm{x}}^2\right)\sec {}^2\left(\sin {4\mathrm{x}}^2\right)\sec {}^2\left(\tan \left(\sin {4\mathrm{x}}^2\right)\right)\sec \left(\tan \left(\tan \left(\sin {4\mathrm{x}}^2\right)\right)\right)))...$$

Commented by sandy_delta last updated on 10/Sep/20

$$\mathrm{how}\mathrm{do}\mathrm{you}\mathrm{get}\mathrm{the}\mathrm{answer}\mathrm{Sir}?$$

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