OpenStudy (anonymous):

Find the derivative f(x) = -7/x at x = -3

hartnn (hartnn):

do you know the general formula ? derivative of x^n is ?

OpenStudy (anonymous):

isn't it the slope formula?

hartnn (hartnn):

nah, if \(f(x) = x^n \\ \large f'(x) = n x^{n-1}\) heard of it ?

OpenStudy (anonymous):

no. Do I just plug in x?

hartnn (hartnn):

-7/x since -7 is constant, it can be thrown out of the derivative \((-7/x)' = (-7) (1/x)' = -7 (x^{-1})'\) and for derivative of x^(-1) you can use that general formula just plug in n = -1

OpenStudy (anonymous):

-7/-1?

hartnn (hartnn):

no....plug in n = -1 in n x^(n-1)

OpenStudy (anonymous):

(-1) (-3)^(-1-1) I don't get it.

hartnn (hartnn):

|dw:1397678538186:dw| got this ?