Use the Product Rule twice to find a formula (fg) in terms of f and g and their first and second derivatives.

Question

likvau · Accepted Answer

Step 1Product rule in derivative: [A(x).B(x)]&#039; = A(x).B&#039;(x) + A&#039;(x).B(x)Step 2To find (fg)&#039;&#039; = ?     (fg)&#039;&#039; = [(fg)&#039;]&#039;= [f.g&#039; + f&#039;.g]&#039;= [(f.g&#039;) + (f&#039;.g)]&#039;= (f.g&#039;)&#039; + (f&#039;.g)&#039;= (f.g&#039;&#039; + f&#039;.g&#039;) + (f&#039;.g&#039; + f&#039;&#039;.g)= f.g&#039;&#039; + f&#039;.g&#039; + f&#039;.g&#039; + f&#039;&#039;.g= f.g&#039;&#039; + 2f&#039;.g&#039; + f&#039;&#039;.gStep 3(fg)&#039;&#039; = f.g&#039;&#039; + 2f&#039;.g&#039; + f&#039;&#039;.g

Use the Product Rule twice to find a formula (fg)'' in terms of f and g and their first and second derivatives.

Answered question

Answer & Explanation

New Questions in Calculus 1