How do you differentiate # (4x − 2) / (x^2 + 1)#?

Answer 1

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

To differentiate this, use the quotient rule:

#(f/g)^'=(f^'g-fg^')/g^2#

In this case, #f=4x-2# and #g=x^2+1#. It then follows that #f^'=4# and #g^'=2x#. Plugging all of these expressions into the formula gives

#(4(x^2+1)-(4x-2)(2x))/(x^2+1)^2=(-4x^2+4x+4)/(x^2+1)^2#

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Answer 2

Emilia Aguilar

To differentiate the expression (4x − 2) / (x^2 + 1), you can use the quotient rule of differentiation. The quotient rule states that if you have a function in the form of f(x) / g(x), then the derivative is (f'(x)g(x) - f(x)g'(x)) / (g(x))^2.

So, for the expression (4x − 2) / (x^2 + 1):

f(x) = 4x - 2 g(x) = x^2 + 1

f'(x) = 4 (derivative of 4x - 2 with respect to x) g'(x) = 2x (derivative of x^2 + 1 with respect to x)

Now, plug these values into the quotient rule:

((4)(x^2 + 1) - (4x - 2)(2x)) / (x^2 + 1)^2

Simplify this expression to get the final answer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.