Question

The directional derivative of the following function at $(1,2)$ in the direction $(4\hat{i}+3\hat{j})$ is: $f(x,y)=x^2+y^2$

• A. $4/5$
• B. $4$
• C. $2/5$
• D. $1$

Answer 1

The correct option is B $4$

$\overrightarrow{a}=4\hat{i}+3\hat{j}$
$f(x,y)=x^2+y^2$
$▽f=2x\hat{i}+2y\hat{j}$
$(▽f{)}_{(1,2)}=2\hat{i}+4\hat{j}$
Directional derivative=
$▽f.\hat{a}$
$=(2\hat{i}+4\hat{j}).\left(\frac{4\hat{i}+3\hat{j}}{5}\right)=\frac{8+12}{5}=4$