A Meta

3a Lista de Matem´tica Aplicada - Derivadas a Prof. S´vio Mendes Fran¸a a c
1. Sabendo que a fun¸˜o derivada de f (x) = xn ´ a fun¸˜o f (x) = nxn−1 e usando as duas primeiras ca e ca proprieades operat´rias das derivadas, determine a fun¸˜o derivada de: o ca
(a) f (x) = 2x + 4
(b) f (x) = 3x − 2
(c) f (x) = x3 − 2x2 − 2x + 4
(d) f (x) = x3 + 3x2 − 3x − 6
(e) f (x) = 5x3 + 2x2 + 2x − 6
(f) f (x) = 4x3 + 3x2 − 2x − 3
(g) f (x) = 2x2 + 4x + 3
(h) f (x) = 3x4 + 2x3 − 5x2 + 3x + 4
(i) f (x) = −x2 − 5x − 4
(j) f (x) = x4 + x3 + 2x2 − x − 1

2. Calcule a derivada de:
1
x2
1
f (x) = 3 x −4 f (x) = 3 x 2 f (x) = 3
5x
√ f (x) = x

(a) f (x) =
(b)
(c)
(d)
(e)

√
(f) f (x) = 3 x
√
(g) f (x) = x5
(h) f (x) =

√
3

x

√
4

x3
√
4
(j) f (x) = 2 x3
(i) f (x) =

2
(k) f (x) = √ x 1
(l) f (x) = √ x3 2
(m) f (x) = √
3 x
2x
(n) f (x) = √ x 1

3. Calcule a derivada de:
(a) f (x) =

2
2
3
− 3
+
x 3x2
4x

(b) f (x) = 5x2 + 3x + 4 +
(c) f (x) =
(d) f (x) =
(e) f (x) =
(f) f (x) =
(g) f (x) =
(h) f (x) =

−4
5
− 3
3
x x 3
2
+√
2
x x 1
1
3
√ −√ + 2
3
2
3
x x x
3
2 x + 2x
2x
√
4x4 − x2 − x
3x2
2
3x − 4x
√
x
√
√
3
x2 + x + x − 3
√
x

4. Usando a regra do produto, calcule a derivada de:
(a) f (x) = xcosx
(b) f (x) = ex senx
(c) f (x) = x2 lnx
(d) f (x) = x3 − 2x + 3 senx
√
(e) f (x) = x2 x
√
3
(f) f (x) = x2 cosx
(g) f (x) =

5x +

1 x2 √

x

(h) f (x) = (3x + 4) x2 + 2x

5. Usando a regra do quociente, calcule a derivada de:
(a) f (x) =
(b) f (x) =
(c) f (x) =
(d) f (x) =
(e) f (x) =
(f) f (x) =
(g) f (x) =
(h) f (x) =

x2 x2 − 2x
√
x−x
2x2
senx x2 x e x
2 − 3x
√
3 x 2x + 3
√
x3 senx cosx
2x3 − x2 + 3x − 2 x2 + 1

2

6. Usando a regra da cadeia, calcule a derivada de:
(a) f (x) = sen x2 + 2
(b) f (x) = x3 + 2x − 3

3

3

(c) f (x) = ex

(d) f (x) = ln (2x + 3)
(e) f (x) = cos3 x
(f) f