Q. 13 - Calculus

Question

Given that f,g,h are functions with values f(2)=1, g(2)=-4, h(2)=3 and point -derivatives f'(2)=3, g'(2)=0, h'(2)=-1 Calculate

$\left(fh\right)\text{'}\left(2\right)$

Step-by-Step Solution

Answer

The value is $\left(fh\right)\text{'}\left(2\right)=8$

Step 1: Given information

We are giventhat f,g,h are functions with values f(2)=1, g(2)=-4, h(2)=3 and point -derivatives f'(2)=3, g'(2)=0, h'(2)=-1 

Step 2: Calculate the value

We are given $\left(fh\right)\text{'}\left(2\right)$

Which can be simplified as

$$\begin{gathered} f\left(2\right)h\text{'}\left(2\right)+f\text{'}\left(2\right)h\left(2\right) \\ =1(-1)+3\left(3\right) \\ -1+9 \\ =8 \end{gathered}$$

Hence the value $\left(fh\right)\text{'}\left(2\right)=8$