Question

6.) Find the indicated derivative

Answer 1

$\frac{x(14x+26)'-(14x+26)x'}{x^{2}} = \frac{x(14)-(14x+26)*1}{x^{2}}= - \frac{26}{x^{2}}$

Answer 2

For this derivative, we'll use the quotient rule. The quotient rule uses the following formula:

$\frac{d}{dx} \frac{f}{g} = \frac{(g)(f') - (f)(g')}{g^2}$

Apply this rule to the expression in the question:

$f(x) = 14x + 26$
$g(x) = x$

$\frac{d}{dx} \frac{14x + 26}{x} = \frac{(x)(14) - (14x + 26)(1)}{x^2}$

$x \cdot 14 = 14x$
$(14x + 26) \cdot 1 = (14x \cdot 1) + (26 \cdot 1) = 14x + 26$
$14x - (14x + 26) = 14x - 14x - 26 = -26$

$\frac{(x)(14) - (14x + 26)(1)}{x^2} = \frac{-26}{x^2} =\boxed{ -\frac{26}{x^2} }$

The derivative will be -(26 / x^2).