Find the directional derivative of f (x, y) = 3x² – 4xy³ + 3y²- 4x in the direction of u =cos()i+ sin()j andsimplify.

Answered: Find the directional derivative of f…

Find the directional derivative of f (x, y) = 3x² – 4xy + 3y2 - 4x in the direction ofu = cos( 플)i+ sin(플)j and simplify.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.4: Derivatives Of Exponential Functions

Problem 9E: Find derivatives of the functions defined as follows. y=3e2x2

See similar textbooks

Related questions

Q: Find the directional derivative of z = f (x, y) = x²y³ – 3y² at (-3,4) in the direction of the…

A: Use directional derivative formula which is mentioned in solution.

Q: EX Prove that the directional derivative of f(x, y) = y² + 2xy³ + x²y² at point (0, 1) in the…

A: What is Directional Derivative: The directional derivative of a scalar function represents the rate…

Q: What is the directional derivative of f(x, y, z) = bx²y²z² + x² + y² + z² in the direction of v =…

Q: find the directional derivative of f(x,y,z)=3e^xcos(yz) at P(0,0,0) in the direction of A=2i+j-2k

A: First find out the partial differentiation of f(x,y,z) and then put the values (0,0,0) and then for…

Q: Find the directional derivative of the function f(x, y) = 1+5x/ỹ at the point (5, 1) in the…

Q: Find the directional derivative of f(x, y) = x² sin(2y) at (1, 7/2) in the direction of ở = 3i– 4j.

Q: O Find the directional derivative of f(x, y) = 3x² – 3y² in the direction from P(-,0) to Q(0, 1).

A: Point is given so first find the direction unit vector then dot product with divergent of f(x,y)…

Q: Find the directional derivative of f(x, y) = 3x2 − 2y2 at (−3/ 4, 0) in the direction from P(−3/4,…

A: The directional derivative is the scalar product of the derivative of the function to the vector…

Q: Find the directions in which the directional derivative of f (x, y) = ye*y at the point (0,2) has…

Q: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

Q: What is the directional derivative of the function f(x.y)-2xy-3y at point p.- (5,5) in the direction…

A: To find: The directional derivative of the function f(x,y)=2xy-3y2 at point P=(5,5) in the direction…

Q: Find the directional derivative of f(x, y) = x2y3 + xy2 in the direction ~v =< −3, 7 > at the…

A: f(x, y) = x2y3 + xy2 Please see the white board for the partial derivatives at the point (-1,…

Q: What is the directional derivative of f(x,y)= 2x²+3y² at the point (1,1) in the direction of v =i-j?…

Q: Find the derivative of the function f(z, u) = =*y – 4y° at the point Po(2, 1) in the direction of =…

Q: Find the derivative of f at point P in the direction of u. f(x, y, z) = 6x² + 2y – 7z?, P = (8,–6,…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the directional derivative of f(x, y) = 4x^3 + 3y^2at the point (2, -1) in the direction of v =…

A: The directional derivative of a function can be obtained by evaluating the dot product between the…

Q: Find the directional derivative of f(x,y) = x²y at the point P(-5,5) in the direction of v = 3i –…

Q: Find the directional derivative of the function f(x,y) = y² Inx at the point (1,2) in the direction…

A: Given function, f(x,y)=y2 ln x Point 1,2 and vector u=3,4 The unit vector of u is…

Q: Find the directions in which the directional derivative of f(x, y) = ye at the poist (0, 2) has the…

Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: Find the directional derivative of f(x, y, 2) = xz+ y?, at (1, 2, 3) in the direction of i = i+j+ k.…

Q: Find the directional derivative of Ax,y,2) = xy+ 4y²z+3xz? at the point (3,-1,2) in the direction of…

Q: Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in the direction a.…

Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

Q: What is the derivative of h(x, y) = e"Y at (2, 3) in the direction at an angle of 7 from the…

Q: Find the directional derivative of f(x, y) = Vxy at P(9, 1) in the direction from P to Q(12, -3).…

A: Given that: f(x,y)=xy at P(9,1) in the direction of Q(12,-3)

Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

Q: Find the directional derivative of f(x, y) = x 2 + 4y 2 at the point P = (3, 2) in the direction…

A: Given, f(x,y)=x2+4y2 at the point P=(3,2)

Q: Find the directional derivative of the function f(x, y) = x² + y³ at the point (2, 1) in the…

Q: Find the directional derivative of f(x, y) = 3x² - y² + 5xy at (2,-1) in the direction of -3i - 4j.

A: given function f(x,y)=3x2-y2+5xy given point (2, -1) given direction u→=-3i-4j We have to find the…

Q: Find the directional derivative of f(x, y) = Vxy at P(3, 3) in the direction from P to Q(6, -1).…

A: Using partial derivatives at (3,3) in direction of PQ.

Q: What is the directional derivative of the function f(x,y) = 2xy- 3y2 at point po= (5,5) in the…

A: Givenf(x,y)=2xy-3y2 ; p0=(5,5) ; u=4i+3jWe need to find directional derivative Duf(5,5)where…

Q: Find the directional derivative of f(x, y, z) = xy + z 3 at the pointP = (3, -2, -1) in the…

A: fx, y, z=xy+z3, P=3, -2, -1. Now, ∂f∂x=y·1+0=y∂f∂y=x·1+0=x∂f∂z=0+3z2=3z2 Now, ∇fx, y, z=∂f∂x, ∂f∂y,…

Q: Prove that the directional derivative of f(x, y) = y + 2xy³+x²y2 at point (0, 1) in the direction…

A: The gradient is just the vector of partial derivatives. The partial derivatives of f at the point…

Q: Find the directional derivative of f (x, y) = e" /Ty at the point (1,16) in the direction of the…

A: From the given problem: fx,y=exxy ; p1,16 And the direction of the negative y- axis means :…

Q: The directional derivative of f=8x²y-2xy²+3z at point P(1,1,2) in the direction 2âg+2ây-âz is

A: First we find the gradient of the function f and then unit vector.

Q: Find the directional derivative of f(x, y) = In(e- 2y) at the point (0, 0) in the direction of 3i +…

Q: Find the directional derivative of f(x, y, z) = x²y²z + 4xz at (-1,2,1) in the direction 2i + j +…

A: We have to find the directional derivative of f(x, y, z)=x2y2z+4xz at (-1, 2, 1) in the direction…

Q: Find the directional derivative of the function in the direction of u = cos(e)i + sin(@)j. F(x, y)…

A: Explained below

Q: Find the directional derivative of f (x,y)=2x² cos 2y at 2, in the direction of 3i+4j. 2 8 (a)- 5 8…

Q: Find the directional derivative of f(z, y) = In(e" - 3y) at the point (0,0) in the direction of 3i +…

Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2xy - 3y2, P0(5, 5), u =…

Q: Find the derivative of f(x, y) = (2x – y°, sin(ry), r²y*)

A: Given f(x,y)=2x-y3,sin(xy),x2y3 differentiate f(x , y) with respect to x we get…

Q: Find the directional derivative of f(x,y) v = 3i – 4j. x² sin 2y at (1, 7/2) in the direction of |

Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = 8x-4xy+3y,…

Q: find the directional derivative of f (X, 4) = 3x² + 5y² at the poin t (1,-1) in the dccection of V…

Q: Find the derivative of f(x,y) = xe² +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j .

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The directional derivative of f(r, y) =-e" cos y at (0, 5) in the direction of v = (-6, 8) is

A: Given that fx,y=-excos y at0,π4and v=-6,8

Question

Find the directional derivative of f (x, y) = 3x² – 4xy³ + 3y²
- 4x in the direction of u =
cos()i+ sin()j and
simplify.

Expert Solution

Step 1 Definition

Directional derivative of f in the direction of u is given by

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.