Vamos aplicar:
y ' = 1 36 x 9 x 2 - 2 4 - 9 x 2 + 2 27 arcsen 3 x 2 ' = 1 36 x 9 x 2 - 2 4 - 9 x 2 ' + 2 27 arcsen 3 x 2 ' = 1 36 9 x 3 - 2 x 4 - 9 x 2 ' + 2 27 arcsen 3 x 2 '
Vamos resolver a primeira derivada:
1 36 9 x 3 - 2 x 4 - 9 x 2 ' = f ' x g x + g ' x f x = 1 36 9 x 3 - 2 x ' 4 - 9 x 2 + 4 - 9 x 2 ' 1 36 9 x 3 - 2 x = 1 36 3 ⋅ 9 x 3 - 1 - 2 x 1 - 1 4 - 9 x 2 + 1 2 4 - 9 x 2 1 2 - 1 4 - 9 x 2 ' 1 36 9 x 3 - 2 x = 1 36 27 x 2 - 2 x 0 4 - 9 x 2 + 1 2 4 - 9 x 2 - 1 2 0 - 2 ⋅ 9 x 2 - 1 1 36 9 x 3 - 2 x = 1 36 27 x 2 - 2 ⋅ 1 4 - 9 x 2 + - 9 x 4 - 9 x 2 1 36 9 x 3 - 2 x = 27 x 2 - 2 4 - 9 x 2 36 + - 9 x 9 x 3 - 2 x 36 4 - 9 x 2 = 27 x 2 - 2 4 - 9 x 2 - 9 x 9 x 3 - 2 x 36 4 - 9 x 2 = 108 x 2 - 243 x 4 - 8 + 18 x 2 - 81 x 4 + 18 x 2 36 4 - 9 x 2 = 144 x 2 - 324 x 4 - 8 36 4 - 9 x 2 = 144 x 2 - 324 x 4 - 8 36 4 - 9 x 2 = 36 x 2 - 81 x 4 - 2 9 4 - 9 x 2
Agora a segunda:
2 27 arcsen 3 x 2 ' = 2 27 ⋅ 1 1 - 3 x 2 2 ⋅ 3 x 2 ' = 2 27 1 - 9 x 2 4 ⋅ 3 2 x 1 - 1 = 2 27 4 - 9 x 2 4 ⋅ 3 2 x 0 = 2 27 4 - 9 x 2 4 ⋅ 3 2 ⋅ 1 = 1 9 4 - 9 x 2 2 = 2 9 4 - 9 x 2