Question
Find the gradient of the function.$$f(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}}$$
Step 1
The partial derivative of the function with respect to x is given by: $$\frac{\partial f}{\partial x} = \frac{1}{2\sqrt{x^{2}+y^{2}+z^{2}}} \cdot 2x = \frac{x}{\sqrt{x^{2}+y^{2}+z^{2}}}$$ Show more…
Show all steps
Your feedback will help us improve your experience
Lucas Finney and 86 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the gradient of the given functions. $$ f(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}} $$
Multivariable Functions
The Chain Rule and the Gradient
Find the gradient of the function. $$f(x, y, z)=1 /\left(x^{2}+y^{2}+z^{2}\right)$$
Differentiating Functions of Several Variables
Gradients and Directional Derivatives in Space
Find the gradient of the function. $$f(x, y, z)=y z^{2} /\left(1+x^{2}\right)$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
