Derivatives)

Exercise

1.

Find the derivative of the following functions using the definition of derivative.

(a)

$${f(x) = \cos{3x}}$$

(b)

$${f(x) = (x + 2)^{n} \ (n : \mbox{integer})}$$

2.

Find the defivative of the following funciton．

(a)

$${f(x) = x^4}$$

(b)

$${f(x) = e^{x}}$$

3.

Find the right-hand and left-hand derivative at $x = 0$.

(a)

$${f(x) = \vert x^2 + x\vert}$$

(b)

$${f(x) = \left\{\begin{array}{ll} x^2 \sin{\frac{1}{x}}, & x \neq 0\\ 0, & x = 0 \end{array}\right.}$$

(c)

$${f(x) = \sqrt{x^3 + x^2}}$$