Differentiate:

f(x) = 2x-(x^2+1)^7 / 3

the answer choices are
1) f'(x) = 2-x / 3(x^2+1)^6
2) f'(x) = 2/3 - 14/3 x(x^2+1)^6
3) None of the above

so the answer would number 1 correct?

looks pretty straightforward to me

y = 2x - (1/3)(x^2 + 1)^7
dy/dx = 2 - (7/3)(x^2 + 1)^6 (2x)
= 2 - (14/3)x(x^2+1)^6

neither of their answers are correct

In google type: calc101

When you see list of results click on:

Calc101com Automatic Calculus,Linear Algebra and Polynomials

When page be open clik option: derivatives

When this page be open in rectacangle type:

2x-(x^2+1)^7/3

and click options DO IT

You will see solution step-by-step

By the way on this site you can practice any kind of derivation.

To differentiate the given function, use the quotient rule. 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 both differentiable functions, then the derivative of f(x) is given by:

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

Let's differentiate the given function step by step:

Function: f(x) = (2x - (x^2 + 1)^7) / 3

Step 1: Find the derivative of the numerator.
The derivative of 2x is simply 2.
For the second part, apply the chain rule. The derivative of (x^2 + 1)^7 with respect to x is: 7(x^2 + 1)^6 * 2x.

So, the derivative of the numerator is: 2 - 14x(x^2 + 1)^6

Step 2: Find the derivative of the denominator.
The derivative of 3 is 0.

Step 3: Apply the quotient rule.
Using the quotient rule formula, we have:

f'(x) = [2 - 14x(x^2 + 1)^6 * 3] / (3)^2
= [2 - 42x(x^2 + 1)^6] / 9

Now, let's compare the simplified answer choices:

1) f'(x) = 2 - 42x(x^2+1)^6 / 9
2) f'(x) = 2/3 - 14/3 x(x^2+1)^6

From the steps above, we can see that the correct answer is 2) f'(x) = 2/3 - 14/3 x(x^2+1)^6.

Therefore, the correct answer is option 2.