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Question

Solve y=tan15axa26x2, find dydx

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Solution

y=tan1(5axa26x2)
tany=5axa26x2sec2ytan2y=1
(sec2y)dydx=5a(a26x2)(12x)(5ax)(a26x2)2
[1+(5axa26x2)2]dydx=5a330ax2+60ax2(a26x2)2
[a4+36x4+13a2x2(a26x2)2]dydx=5a3+30ax2(a26x2)2
[(a4)+36x4+13a2x2]dydx=5a(a2+6x2)
(a2+9x2)(a2+4x2)dydx=5a(a2+6x2)
dydx=5a(a2+6x2)(a2+9x2)(a2+4x2)
dydx=3a(a2+4x2)+2a(a2+9x2)(a2+9x2)(a2+4x2)
dydx=3aa2+9x2+2aa2+4x2

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