Question

Find the derivative of f(x) = -3/x at x = -4.

Answer 1

sorry can't help you on this one, im only 15 haven't done derivatives

Answer 2

\[\Large f(x) = -3x^{-1}\]Find the derivative now.

Answer 3

i will bet you have to do this by hand, not by the power rule

Answer 4

Use the quotient rule to differentiate:\[\bf if \ f(x)=\frac{ g(x) }{ h(x) } \ then \ f'(x)=\frac{ g'(x)h(x)-g(x)h'(x) }{ [h(x)]^2 }\]After obtaining the derivative, just plugin x = -4 and evaluate.

You could also do what @saifoo.khan did and use rational exponents to differentiate more easily using Power rule.

Answer 5

quotient rule?!

Answer 6

-3/(-4)
like this??

Answer 7

\[\lim_{x\to -4}\frac{-\frac{3}{x}+\frac{3}{4}}{x+4}\]

Answer 8

from your previous questions i am assuming that you have to do this by the definition

Answer 9

3/4
3/16
16/3
4/3

Answer 10

those are the answer choices

Answer 11

i made a typo, it is
\[\lim_{x\to -4}\frac{-\frac{3}{x}-\frac{3}{4}}{x+4}\]
the answer is easy to come by, i think you need the method

Answer 12

the easy way to do it is to say the derivative of \(-\frac{3}{x}\) is \(\frac{3}{x^2}\) and then plug in \(x=-4\) to get \(\frac{3}{16}\)

Answer 13

the method is to compute the limit i wrote above \[\lim_{x\to -4}\frac{-\frac{3}{x}-\frac{3}{4}}{x+4}\]

Answer 14

so what about this one???

Find the derivative of f(x) = -10x2 + 4x at x = 11.

-216

-196

-176

-363

Answer 15

most of it is algebra
simplify the expression to get \[\frac{\frac{-3(x+4)}{4x}}{x+4}\] then cancel the \(x+4\) to get
\[\frac{-3}{4x}\] then let \(x=-4\)

Answer 16

\[f(x) = -10x^2 + 4x\]
\[f'(x)=-20x+4\] find \[f'(11)\] is the easy way

Answer 17

so for the first question its 3/16??
and for the last question its 11???

Answer 18

for the first question it is \(\frac{3}{16}\)
for the last question it is
\[f'(11)\] where \(f'(x)=-2x+4\)

Answer 19

oops i meant \(f'(x)=-20x+4\)

Answer 20

but thats not one of the answers @satellite73

Answer 21

the answers are -216

-196

-176

-363

Answer 22

i will let you compute
\[f'(11)=-20\times 11+4\]

Answer 23

oh ok one sec

Answer 24

so its -216 @satellite73