Question

What is the derivative of -cos(x)?

Answer 1

Answer:

We can use the difference quotient or the power rule.

Lets use the Power Rule first.

$f \: (x) \: = x \: = {x}^{1}$

$f \: (x) \: = 1 {x}^{1 - 1} = 1 {x}^{0} = 1.1 = 1$

Difference quotient

$lim \: = \: \frac{f(x + h) \: - f(x)}{h} = \frac{x + h - x}{h} = \frac{h}{h} = 1$

$Also \: note \: that \: f(x) = x \: is \: a \: linear \: equation \: y = 1x + b. \:  The \: slope \: of \: this \: line \: is \: also \: 1.$