Find the directional derivative of f(x,y) = sin(x+2y) at the point (2, 4) in the direction θ = 3π/4. The gradient of f is: ∇f = ⟨cos(x+2y), 2cos(x+2y)⟩ ∇f(2,4) = ⟨cos(10), 2cos(10)⟩ The directional derivative is: ???
Added by Rebecca J.
Step 1
We already have the gradient formula: ∇f = 〈cos(x+2y), 2cos(x+2y)〉 Now, we need to plug in the point (2, 4) into the gradient formula: ∇f(2,4) = 〈cos(2+2(4)), 2cos(2+2(4))〉 = 〈cos(10), 2cos(10)〉 Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 101 other Calculus 1 / AB 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 directional derivative of the function in the direction of $\mathbf{u}=\cos \theta \mathbf{i}+\sin \theta \mathbf{j}$. $$ f(x, y)=x^{2}+y^{2}, \quad \theta=\frac{\pi}{4} $$
Functions of Several Variables
Directional Derivatives and Gradients
Find the directional derivative of $f$ at the given point in the direction indicated by the angle $\theta$ . $f(x, y)=x^{2} y^{3}-y^{4}, \quad(2,1), \quad \theta=\pi / 4$
Multivariable Calculus
Directional Derivatives and the Gradient Vector
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y) = 7e^x sin(y), (0, π/3), v = (-10, 24)
Adi S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD