Respostas

  • Usuário do Brainly
2014-06-10T16:08:10-03:00
F(x)=tgx
f-¹(x)=arctgx
f(f-¹(x))=x
f(f-¹(x))'=x'
f'(f-¹(x)).f-¹'(x)=1
f-¹'(x)=1/f'(f-¹(x))

f'(x)=sec²x = tg²x+1
f-¹(x)=arctgx

f-¹'(x)=1/tg²(arctgx)+1
f-¹'(x)=1/x²+1
~~arctg'x=1/x²+1 (Só uma demonstração da derivada da inversa.)

a)
f(x)=arctg(lnx)
f'(x)=arctg'(lnx).lnx'
f'(x)=1/(lnx)²+1 . 1/x
f'(x)=1/x.(lnx)²+x

b)
f(x)=sen³3x
f'(x)=3.cos²3x

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