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

y=sec{sec[tan(tan(sin 4x^2 ))]}  (dy/dx) = ?

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

Commented by MJS_new last updated on 10/Sep/20

f_1 (f_2 (f_3 (f_4 (f_5 (f_6 (x))))))=  =f_1 ′(f_2 (f_3 (f_4 (f_5 (f_6 (x))))))×  ×f_2 ′(f_3 (f_4 (f_5 (f_6 (x)))))×  ×f_3 ′(f_4 (f_5 (f_6 (x))))×  ×f_4 ′(f_5 (f_6 (x)))×  ×f_5 ′(f_6 (x))×  ×f_6 ′(x)

$${f}_{\mathrm{1}} \left({f}_{\mathrm{2}} \left({f}_{\mathrm{3}} \left({f}_{\mathrm{4}} \left({f}_{\mathrm{5}} \left({f}_{\mathrm{6}} \left({x}\right)\right)\right)\right)\right)\right)= \\ $$$$={f}_{\mathrm{1}} '\left({f}_{\mathrm{2}} \left({f}_{\mathrm{3}} \left({f}_{\mathrm{4}} \left({f}_{\mathrm{5}} \left({f}_{\mathrm{6}} \left({x}\right)\right)\right)\right)\right)\right)× \\ $$$$×{f}_{\mathrm{2}} '\left({f}_{\mathrm{3}} \left({f}_{\mathrm{4}} \left({f}_{\mathrm{5}} \left({f}_{\mathrm{6}} \left({x}\right)\right)\right)\right)\right)× \\ $$$$×{f}_{\mathrm{3}} '\left({f}_{\mathrm{4}} \left({f}_{\mathrm{5}} \left({f}_{\mathrm{6}} \left({x}\right)\right)\right)\right)× \\ $$$$×{f}_{\mathrm{4}} '\left({f}_{\mathrm{5}} \left({f}_{\mathrm{6}} \left({x}\right)\right)\right)× \\ $$$$×{f}_{\mathrm{5}} '\left({f}_{\mathrm{6}} \left({x}\right)\right)× \\ $$$$×{f}_{\mathrm{6}} '\left({x}\right) \\ $$

Commented by sandy_delta last updated on 10/Sep/20

thanks very much Sir

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

Answered by bobhans last updated on 10/Sep/20

8xcos (4x^2 )sec^2 (sin 4x^2 )sec^2 (tan (sin 4x^2 ))sec (tan (tan (sin 4x^2 )))))...

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

Commented by sandy_delta last updated on 10/Sep/20

how do you get the answer Sir?

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

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