In getting the derivative of a rational function,

lenniellemae.decastro

lenniellemae.decastro

Answered question

2022-06-27

In getting the derivative of a rational function, just get the derivative of the numerator divided by the derivative of the denominator. TRUE or FALSE.

Answer & Explanation

nick1337

nick1337

Expert2023-05-29Added 777 answers

The statement In getting the derivative of a rational function, just get the derivative of the numerator divided by the derivative of the denominator is FALSE.
When differentiating a rational function, the derivative of the numerator divided by the derivative of the denominator does not provide the correct result. The correct method for differentiating a rational function involves using the quotient rule.
The quotient rule states that for a function of the form f(x)=g(x)h(x), where g(x) and h(x) are differentiable functions, the derivative is given by:
f(x)=g(x)h(x)g(x)h(x)(h(x))2
As we can see, the derivative of a rational function involves the derivatives of both the numerator and denominator, as well as their respective products.
Therefore, the correct statement is that when differentiating a rational function, we cannot simply take the derivative of the numerator divided by the derivative of the denominator. We must use the quotient rule to obtain the correct result.

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