Calcule a derivada da função f(X)= X³/senx
Soluções para a tarefa
(a) f(x) = 10x
2 − x + 1
Resposta: f
0
(x) = 20x − 1, f
00(x) = 20
(b) f(x) = x
3
4 +
1
x
Resposta: f
0
(x) =
3
4
x
− 1
4 − x
−2
, f
00(x) = −
3
16x
− 5
4 + 2x
−3
(c) f(x) =
√
2x + 1
Resposta: f
0
(x) = √
1
2x+1 , f
00(x) = −(2x + 1)− 3
2
(d) f(x) =
√
2x + 1
Resposta: f
0
(x) = √
1
2x
, f
00(x) = −(2x)
− 3
2
(e) f(x) =
1
x
10
Resposta: f
0
(x) =
−10
x11 , f
00(x) =
110
x12
(f) f(x) =
√
50
Resposta: f
0
(x) = f
00(x) = 0
(g) f(x) =
√
50x
Resposta: f
0
(x) =
√
50
2
x
− 1
2 , f
00(x) =
√
50
4
x
− 3
2
(h) f(x) =
e
2
x
3
Resposta: f
0
(x) = −
3e
2
x4
, f
00(x) =
12e
2
x5
(i) f(x) =
e
2x
x
3
Resposta: f
0
(x) = 2e
2xx
−3 − 3e
2xx
−4
,
f
00(x) = 4e
2xx
−3 − 6e
2xx
−4 − 6e
2xx
−4 + 12e
2xx
−5
(j) f(x) = e
x+1
Resposta: f
0
(x) = e
x+1
, f
00(x) = e
x+1