Directional Derivatives

Practice Questions

Calculus 3 › Directional Derivatives

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$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=2^{(x^{4})}e^{(y^{2})}cos(z)\&\text{In the direction of }\overrightarrow{v}=(0,-4,-9).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=\frac{(2^{(z^{4})}x)}{y}- 3zcos(y)\&\text{In the direction of }\overrightarrow{v}=(-20,-3,0).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=\frac{(e^{(x)}ln(z))}{y}- 5e^{(x^{2})}e^{(y)}cos(z)\&\text{In the direction of }\overrightarrow{v}=(-4,-15,0).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=- 2cos(z^{3})tan(y) - 3^xsin(z^{2})e^{(y^{2})}\&\text{In the direction of }\overrightarrow{v}=(-4,-18,0).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=\frac{-{(cos{(x^3)}cos{(y^2)})}}{z}\&\text{In the direction of }\overrightarrow{v}=(0,1,15).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=\frac{{(cos{(x^2)}cos{(z)})}}{y^2}\&\text{In the direction of }\overrightarrow{v}=(0,6,-11).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=\frac{{(cos{(x^2)}ln{(z^2)})}}{y^2}\&\text{In the direction of }\overrightarrow{v}=(-15,0,9).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=3ze^{(x^2)}e^{(y^2)} - cos{(y^2)}e^{(x)}\&\text{In the direction of }\overrightarrow{v}=(0,-1,12).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=sin{(y^2)}cos{(x)}\&\text{In the direction of }\overrightarrow{v}=(-17,7,0).\end{align*}$

$\begin{align*}&\text{Find }D_{\overrightarrow{u}}(x,y,z)\text{ where }f(x,y,z)=6y^2cos{(z^2)}e^{(x^2)}\&\text{In the direction of }\overrightarrow{v}=(-20,-17,19).\end{align*}$

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