61.6k views
1 vote
#9 label A and B parts and solve each separately to come to the result in different ways

#9 label A and B parts and solve each separately to come to the result in different-example-1

1 Answer

4 votes

Solution

9 (a) Using product rule


f(x)=(x-1)(3x+4)
\begin{gathered} u=x-1 \\ (du)/(dx)=1 \end{gathered}
\begin{gathered} v=3x+4 \\ (dv)/(dx)=3 \end{gathered}

The product rule formula is quoted below


(dy)/(dx)=u(dv)/(dx)+v(du)/(dx)
\begin{gathered} f^(\prime)(x)=(dy)/(dx)=(x-1)*3+(3x+4)*1 \\ \\ f^(\prime)(x)=3(x-1)+3x+4 \\ f^(\prime)(x)=3x-3+3x+4 \\ f^(\prime)(x)=6x+1 \end{gathered}

9(b) Verifying the resuts of 9(a) by bexpanding the product first and subsequently differentiating


\begin{gathered} f(x)=(x-1)(3x+4) \\ f(x)=3x^2+x-4 \\ \\ f^(\prime)(x)=(dy)/(dx)=6x+1 \end{gathered}

In conclusion , we observe that the results of the derivatives are the same irrespective of the approach used as shown in 9(a) and 9(b) above

User Seop Yoon
by
8.1k points

No related questions found