how do you differentiate using the product rule:((1/x^2)-(3/x^4)) (x+(5x^3))answer: (5+(14/x^2)+(9/x^4))?

Question

I need to know the step of how you did it.
The formula is f(x)g'(x) + g(x)f '(x)

This is a calculus question.

formula is

f(x) = g'(x)f(x) + f"(x)g(x)

I need to know how you did it.

Answer 1

Are you a teacher? Because if you are, can you give me the answers that way I can ask my mom that and be able to figure it out while having the right answer. Can you teach me and help me with the answer? please.

Answer 2

Start with the 4. 4 equals 2 squared as well as 2+2. Then you take the 3/2. 3 halves is what ex-wives will take if you get married and seperated 3 times. So 3/2 & the 4 gives you 16. Good luck.

Answer 3

First we want to simplify this expression, by rewriting division as negative exponents. Negative exponents are much easier to differentiate. Write the problem as:
(x^-2 - 3x^-4)(x + 5x^3)

You could use the chain rule at this point, but since it is a simple binomial, I would distribute to get:
x^-1+ 5x - 3x^-3 -15x^-1

Simplify like terms to get:
-14x^-1 + 5x - 3x^-3

Finally take the derivative, by multiplying the exponent by the coefficient and subtracting one from the exponent:
14x^-2 + 5 + 9x^-4

The derivative may be rewrote as positive exponents, as:
14/x^2 + 5 + 9/x^4

Answer 4

I multiplied this out, rather than use the product rule and I got 5x-2x^-1-3x^-3. If I then differentiate I get 5+2x^-2+9x^-4.

Is there an error in the form of your question?

However, you would do the product rule this way, where the apostrophe stands for the derivative of the function:

(x^(-2)-3x^(-4))*(x+5x^3)'+(x^(-2)-3x^(-4))'*(x+5x^3)

since the derivative of a sum is the sum of the derivatives you then solve inside the parenthesis:

(x^(-2)-3x^(-4))*(1+15x^2)+(-2x^(-3)+12x(-5))*(x+5x^3)

Hopefully it then reduces down if I did it right. This is quite difficult to do while typing rather than on paper.

It is blocking my long lines of typing so I am going to break the above lines into multiple lines for readability.

(x^(-2)-3x^(-4))*(x+5x^3)'
+(x^(-2)-3x^(-4))'*(x+5x^3)

differentiating
(x^(-2)-3x^(-4))*(1+15x^2)
+(-2x^(-3)+12x(-5))*(x+5x^3)

I will let you then do the product and addition part.

I do not have a sheet of paper and it is too easy to make a mistake here.

Answer 5

you simply take the coefficient of the quotient of the first variable in each expressin and divide it by the number of quantities there are in the product.

Answer 6

what do you mean?
you want the steps of how you get to the answer or what?
and what do you mean by formula?

Answer 7

learn something your actually going to use in real life.....computers do these tinings for us now !

Answer 8

huh?

Answer 9

what?