Question

6.) Find the indicated derivative

Answer 1

`(x(14x+26)'-(14x+26)x')/(x^(2)) = (x(14)-(14x+26)*1)/(x^(2))= - (26)/(x^(2))`

Answer 2

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


`(d)/(dx) (f)/(g) = ((g)(f') - (f)(g'))/(g^2)`

Apply this rule to the expression in the question:


`f(x) = 14x + 26`

`g(x) = x`


`(d)/(dx) (14x + 26)/(x) = ((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`


`((x)(14) - (14x + 26)(1))/(x^2) = (-26)/(x^2) =\boxed{ -(26)/(x^2) }`

The derivative will be -(26 / x^2).