how do you differentiate -4/x?

Answer 1

the easiest way to look at this problem is to remember that when you bring an exponent from the bottom of a fraction to the top, then the sign on the exponent changes. In your example, -4/x, x has an exponent of 1 while it's on the bottom, x^1, if you move this to the top, you will have x^-1, giving you -4x^-1. Now you have the form that you learned about derivatives in. Multiply the exponent by the coefficient -4 and get 4, then subtract 1 from the exponent -1 and get -2 just like in normal differentiation. Now, you have 4x^-2. Use the rule that you started with and take the x^-2 to the bottom of the fraction and change the sign giving 4/x^2.
You are probably learning about the quotient rule right now, but it's important to realize that you don't need it sometimes. Good luck!

Answer 2

the respond would be: dy/dx=a million+ (4/(x^2)) from the chain rule you differentiate the outer applications first then you definately bypass to the indoors ones. then, to tell apart a million/x you would be able to desire to think of of it as x^-a million so which you in basic terms subtract an exponent from that and you get x^-2

Answer 3

the formula for differentiation of x^(n) is

nx^(n-1)..................(1)

- 4/x = -4*x^(-1)

here, n = -1,substitute into (1) gives

d(-4*x^(-1)/dx = -4*(-1)*x^(-1-1) = 4*x^(-2)

=4/(x^(2)) as required

i hope that this helps

Answer 4

the derivative is 4/x^2

Answer 5

First rewrite the equation:
-4/x = -4x^-1

Then do like a normal deravative:
dy/dx = 4x^-2 = 4/x^2

PS: I don't know why sweetie is making it so difficult

Answer 6

Hi dear Ned ;

{ as you know if ;
f(x) = u(x) / v(x) ;
f '(x) = u ' v - u v ' / (v) ²
It is the formula you should use.}

-Now ,
f(x) = (-4) / x
let u = -4 , u' = 0 { if "a" is a real number so f '(a) = 0 }
let v = x , v' = 1

-Now follow the formula;
f '(x) = u ' v - u v ' / (v) ²
f '(x) = [ (0 * x) - (-4 * 1)] / (x) ²
f '(x) = [ 0 + 4 ] / (x) ²
f '(x) = ( 4) / (x) ²
f '(x) = 4 / x ²

Good Luck dear....

Answer 7

This is -4x^(-1)

using d/dx(x^n) = nx^(n-1) here n = -1 we get d/dx(-4/x) = 4/x^2

Answer 8

-(4/X) can be rewritten as -(4*x^(-1)).

apply power rule to x^-1... d/dx (x^n) = n*x^(n-1)...

d/dx(x^-1) = (-1)*x^(-1-1) = -x^-2

multiply it by given constant (-4)...

-x^-2 * -4 = +4x^-2

the final answer can be rewritten as 4/x^2...

Answer 9

Use these rules:

d/dx[cf(x)] = cf'(x), for any constant c

d/dx[x^n] = nx^(n-1).

Then, you get

d/dx[-4/x] = -4d/dx[x^-1] = -4(-1)x^(-2)
= 4/x^2.

Answer 10

it becomes 4/xsquared