find the derivative of 3x^4-5x+3/x^4+1

i know that the derivative of the numeratoor would be 12x^3-5 but i'm not sure if its right since it has a denominator i Know i need to do something to it but not sure if to simplify.

You will have to use the quotient rule.

If you don't know what that is ....
you'll have some major catching up to do.

ok, i know what it is had forgotten we use that but its in my notes thanks!!!!

To find the derivative of the given expression, you need to apply the quotient rule, which is used to differentiate a function that is a quotient of two functions.

The quotient rule states that if you have a function of the form f(x) = g(x) / h(x), where g(x) and h(x) are differentiable functions, then the derivative of f(x) can be found using the formula:

f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x))^2

In this case, let's assign:

g(x) = 3x^4 - 5x + 3
h(x) = x^4 + 1

To find the derivative of the numerator, you correctly differentiated it to be g'(x) = 12x^3 - 5.

Now, let's find the derivative of the denominator. Since h(x) = x^4 + 1, the derivative is:

h'(x) = 4x^3

Now, we can apply the quotient rule:

f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x))^2
= ((12x^3 - 5) * (x^4 + 1) - (3x^4 - 5x + 3) * 4x^3) / (x^4 + 1)^2

Simplifying the expression further is possible, but it may not provide much insight into the behavior of the derivative. Therefore, the above expression is the derivative of the given function: f'(x) = ((12x^3 - 5) * (x^4 + 1) - (3x^4 - 5x + 3) * 4x^3) / (x^4 + 1)^2