Question

If $f$ and $g$ are differentiable functions such that $f\left(2\right)=3,f\text{'}\left(2\right)=1,f\text{'}\left(3\right)=7,g\left(2\right)=-5$ and $g\text{'}\left(2\right)=2$, then find the numbers indicated in problem $\left(5f+3g\right)\text{'}\left(2\right)$.

Answer 1

To find the value of $\left(5f+3g\right)\text{'}\left(2\right)$:

If $f$ and $g$ are differentiable functions such that $f\left(2\right)=3,f\text{'}\left(2\right)=1,f\text{'}\left(3\right)=7,g\left(2\right)=-5$ and $g\text{'}\left(2\right)=2$.

Calculate the value of $\left(5f+3g\right)\text{'}\left(2\right)$ in below :

$\begin{array}{rcl}\left(5f+3g\right)\text{'}\left(2\right)& =& 5f\text{'}\left(2\right)+3g\text{'}\left(2\right)\\ & \Rightarrow & \left(5f+3g\right)\text{'}\left(2\right)=5\left(1\right)+3\left(2\right)\left[\text{Substitute values}\right]\\ \therefore \left(5f+3g\right)\text{'}\left(2\right)& =& 11\left[\text{Simplifying}\right]\end{array}$

Hence, the value of $\left(5f+3g\right)\text{'}\left(2\right)$ is $\mathbf{11}$.