Find the derivative of f(x) = negative 3 divided by x at x = -4.

Question

anonymous · Answer

so 3/4?

danjs · Answer

nevermind , i am way off, and was doing the other way , integrate

danjs · Answer

[ 3 / x] ' = 

you can use the quotient derivative rule, or just rewrite the  thing as a negative exponent and do product rule...

[ 3*x^(-1) ] ' =

-1*3*x^(-2)

anonymous · Answer

i am so confused now

danjs · Answer

then put the -2 exponent back 

-3 / x^2

danjs · Answer

oh the prob is -3, so the sign is + sorry


f(x) = -3/x    =   -3*x^(-1)

f ' (x) = 3*x^(-2) = 3/ x^2

anonymous · Answer

so 3/16?

danjs · Answer

the first kinda shortcut rule you learn ,  derivative of a variable to a power

x^n

$$\large \frac{ d }{ dx }x^n  =  n * x^{n-1}$$

danjs · Answer

yeah f ' (-4)

danjs · Answer

unless you have to show something else you learned,

anonymous · Answer

wait i thought the answer is 3/4

danjs · Answer

the derivative is  f '(x) = 3/x^2    , evaluated at x=-4,  f '(-4) = 3/16