帮忙解决下这两个函数的求导不太懂反三角N次方怎么求导y=tg^2(x-2)/lg(x+3)y=2^tgx·arctg^5(3x)

Question

帮忙解决下这两个函数的求导 不太懂反三角N次方怎么求导
y=tg^2(x-2)/lg(x+3)
y=2^tgx·arctg^5(3x)

Answer 1

y=tg²(x-2)/lg(x+3)
y'={2tg(x-2)·sec²(x-2)·lg(x+3)-tg²(x-2)/[(x+3)·ln10]}/[lg(x+3)]²
=2tg(x-2)·sec²(x-2)/lg(x+3)-tg²(x-2)/{(x+3)·[lg(x+3)]²·ln10}
y=2^tgx·arctg^5(3x)
y'=2^tgx·ln2·sec²x·arctg^5(3x)+2^tgx·5arctg^4(3x)·3/(1+9x²)
=2^tgx·arctg^4(3x)·[ln2·sec²x·arctg(3x)+15/(1+9x²)]