Choose one of the following statements, and then explain why it is true or false: A sum's derivative is the total of its derivatives.

Question

Choose one of the following statements, and then explain why it is true or false: A sum&#039;s derivative is the total of its derivatives.

kalupunangh · Accepted Answer

Step 1&amp;nbsp;Let f(x) and g(x) be two functions of x.&amp;nbsp;Their sum is:&amp;nbsp;= f(x) + g(x)&amp;nbsp;Step 2&amp;nbsp;Then we get,&amp;nbsp;(d/dx)[f(x) + g(x)] = (d/dx)[f(x)] + (d/dx)[g(x)]&amp;nbsp;Therefore, we can state that a sum&#039;s derivative is the sum of its derivatives.Hence the given statement is True.

Kirsten Davis · Accepted Answer

Let f(x) and g(x) be two functions.&amp;nbsp;The derivative of the sum of f(x) and g(x) is given by&amp;nbsp;d&amp;nbsp;dx&amp;nbsp;(f(x)+g(x))=d&amp;nbsp;dx&amp;nbsp;f(x)+d&amp;nbsp;dx&amp;nbsp;g(x).&amp;nbsp;As a result, it is true to say that a sum&#039;s derivative is the sum of its derivatives.

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Determine whether each of the following statements is true or

Answered question

Answer & Explanation

New Questions in Calculus 1