For this derivative, we'll use the quotient rule. The quotient rule uses the following formula:
[tex]\frac{d}{dx} \frac{f}{g} = \frac{(g)(f') - (f)(g')}{g^2} [/tex]
Apply this rule to the expression in the question:
[tex]f(x) = 14x + 26[/tex]
[tex]g(x) = x[/tex]
[tex]\frac{d}{dx} \frac{14x + 26}{x} = \frac{(x)(14) - (14x + 26)(1)}{x^2}[/tex]
[tex]x \cdot 14 = 14x[/tex]
[tex](14x + 26) \cdot 1 = (14x \cdot 1) + (26 \cdot 1) = 14x + 26[/tex]
[tex]14x - (14x + 26) = 14x - 14x - 26 = -26[/tex]
[tex]\frac{(x)(14) - (14x + 26)(1)}{x^2} = \frac{-26}{x^2} =\boxed{ -\frac{26}{x^2} }[/tex]
The derivative will be -(26 / x^2).
