OpenStudy (joshmartin16):

Find the derivative of f(x) = 6 divided by x at x = -2.

1 year ago
zepdrix (zepdrix):

Hey Josh, welcome to OpenStudy! Recall that we have a handy exponent rule to help us out on problems like this, \(\large\rm \dfrac{1}{x}=x^{-1}\) From there we can apply our `power rule`. Have you learned about power rule yet? Or do we need to use the limit definition of the derivative at this point?

1 year ago
OpenStudy (joshmartin16):

no i havent

1 year ago
OpenStudy (joshmartin16):

I want to say the answer is -3/2 but im not sure if its correct

1 year ago
zepdrix (zepdrix):

Ok so we'll have some tricky algebra to take care of then.\[\large\rm f(\color{orangered}{x})=\frac{6}{\color{orangered}{x}}\] If we evaluate this function at x+h, instead of x, it looks like this\[\large\rm f(\color{orangered}{x+h})=\frac{6}{\color{orangered}{x+h}}\]

1 year ago
zepdrix (zepdrix):

\[\large\rm \lim_{h\to0}\frac{f(x+h)-f(x)}{h}\quad=\quad \lim_{h\to0}\frac{\frac{6}{x+h}-\frac{6}{x}}{h}\]

1 year ago
OpenStudy (joshmartin16):

so then its not negative its just 3/2

1 year ago
zepdrix (zepdrix):

I dunno, you're jumping straight to the end lol :)

1 year ago
OpenStudy (joshmartin16):

so what numbers do i input

1 year ago
zepdrix (zepdrix):

\[\large\rm f'(-2)\quad=\quad \lim_{h\to0}\frac{\frac{6}{-2+h}-\frac{6}{-2}}{h}\]I guess -2 is our input. You'll want to do something with the numerator, maybe common denominator, ya?

1 year ago
OpenStudy (joshmartin16):

i dont know how to do that

1 year ago
OpenStudy (salsabyl):

The derivative of 1/x is -1/x squared Multiply by the constant 6 and you havevthe general derivative. Then replace the x by -2

1 year ago
OpenStudy (joshmartin16):

ohhhh okay! give me a second

1 year ago
OpenStudy (joshmartin16):

so (-1/-2) * 6

1 year ago
OpenStudy (salsabyl):

Yeah but the -2 is squared

1 year ago
OpenStudy (joshmartin16):

you cant have exponents on the bottom though?

1 year ago
OpenStudy (salsabyl):

Yes you can If you have exponent -2 for example on top, you can transfer it to the bottom but it becomes 2. The sign of the exponent changes but you can have them both on top or bottom

1 year ago
OpenStudy (joshmartin16):

so the answer is 6!

1 year ago
OpenStudy (salsabyl):

The answer is 6 *(-1/(-2)squared)

1 year ago
OpenStudy (salsabyl):

So -6/4

1 year ago
OpenStudy (salsabyl):

So -3/2

1 year ago
OpenStudy (joshmartin16):

awesome thank you!

1 year ago
OpenStudy (salsabyl):

So your first answer was correct

1 year ago
OpenStudy (salsabyl):

You're welcome :)

1 year ago
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