3 7. Find the second partial derivatives for f(x,y)=2x2y + 5y-3x'y 8. Find the total differential for z=-3ycosx+4x3y2 9. Let w-xy* - y, x-In t, y-cos t. Use Chain Rule to find dw/dt when t=0. 10. Find dy/dx implicitly for y5- y4 +3y+x3-6=0. 11. Find a directional derivative for f(x,y)-2+ x2 y2 at (-2,3) in the direction 6 of u cosi sinj 6 12. Find the gradient for f(x,y)=x2y-x In y at (4,1).

Question

Answers for 10-12

3
7. Find the second partial derivatives for f(x,y)=2x2y + 5y-3x'y
8. Find the total differential for z=-3ycosx+4x3y2
9. Let w-xy* - y, x-In t, y-cos t. Use Chain Rule to find dw/dt when t=0.
10. Find dy/dx implicitly for y5- y4 +3y+x3-6=0.
11. Find a directional derivative for f(x,y)-2+
x2
y2 at (-2,3) in the direction
6
of u cosi
sinj
6
12. Find the gradient for f(x,y)=x2y-x In y at (4,1).
View transcribed image text
Expand

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: This is #1

A: Part (a)Consider an object moving along a line with the velocity and initial position.

Q: 150 100 50 20 40 60 3. Suppose that a population develops according to the logistic equation (c) Use...

A: Given that a population develops according to the logistic equation

Q: 2. (4.6) penicillin is sold at a price of $200 per unit. The production cost (in dollars) for x unit...

A: C(x) and P(x) shows the total production cost function and the profit function of penicillin.

Q: skecth the graph a) f(x)=(x-2)2(x+3)   b)f(x) = x2-1/x   c)f(x) = 2x/x2-1    d)f(x) = -23 + 7x2 - 2x...

A: To sketch the graph of given function :

Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = -2 sin (pi...

A: To find the position function we integrate velocity function and use s(0)=2.Answer(A): Position func...

Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...

A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...

Q: Only problem I'm stuck on for this assignment please help!

A: Hi there! The question is having many sub-parts. Since no specification is given, only first three s...

Q: I need help about solving this problem. a) How do I find the time required to reach the maximum amou...

A: Let F be the amount of fertilizer. In 1 minute 1 gallon of solution comes in and 5 gallons of soluti...

Q: Suppose that the demand for a product is given by  p= 1/2ln (5000-q/q+1) where p is in hundreds of d...

A: The elasticity of demand when the quantity demanded (q) is 2 and the price (p) is 3.71 hundreds of d...

Q: The region is formed by the graphs of y 4x and y 12-x. Find the volume of the solid obtained by revo...

A: For the shaded part the outer radius = 12-x and inner radius = 4sqrt(x).  

Q: Find the area, in square units, bounded above by f(x)=6x2 −2x−19 and below by g(x)=7x2 +12x+21.

A: f(x)=6x2 −2x−19 and g(x) = 7x2 +12x+21.As a first step, we need to find the point of intersection of...

Q: 1. Indefinite and definite integrals including trigonometric functions and ones that will require th...

A: a. Integrate the given indefinite integral with respect to x as follows.

Q: How do I solve this differential equation using P(x), Q(x) and v(x)?

A: The given differential equation is,

Q: lim x→5 f(x) where f(x)= { 7x-10 if x<5; 25 if x>=5

A: To find the limit x->5 f(x), we have to find the right and left limit of x=5 first. 

Q: Find the derivative of y with respect to x.

A: Given:The function 

Q: Limit as x approaches 2 of (x3-8)/(x-2)

A: Obtain the value of the limit as follows.

Q: The DeWitt Company has found that the rate of change of its average cost for product is C'(x)=(1/4)-...

A: Given information:The DeWitt Company has found that the rate of change of its average cost for produ...

Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and...

A: The equation of the plane is

Q: Need help solving the equation that is attached

A: x->4^+ means x is slightly greater than 4. That means we have to use the part when x>4 to find...

Q: The sales of a product S(in thousands of dollars) are given by S= 600x/x+40 where x is the advertisi...

A: Given:The function that repesents the sales of a product S is  

Q: Evaluate the integral. Please refer to image.

A: Obtain curl F as follows.

Q: Please show as much steps as possible as I am doing my best to fully understand how to solve these t...

A: Given function is, 

Q: The equation of the line tangnet to the graph of 24e^x at x=2?

A: Find the derivative of the given function.

Q: If l0g x=0.35 and fog6N0.5, evaluate the fo llowig expression.

A: Here, we use the above log rules.

Q: A drag racer accelerates at a(t) = 84 ft/s^2. Assum v(0) and s(0) = 0.

A: Since we are entitled to answer up to 3 sub-parts, we’ll answer the first 3 as you have not mentione...

Q: Help on #2

A: To find the arc length of r(t)=i+tj+2tk in the interval [1,2]

Q: Evaluate the following integral as written. Please refer to attached image.

A: It's  aquestion of double integral. We will first evalaute the integral with respect to x, put the l...

Q: If fx)x3x+1 then fx) (In x]3x (3x+1}x3x (2x+ In xr3x+ 1 3x13r 3 Inx 3x+13 In x

A: Note:Hi there! Thank you for posting the question. The first line in the image is not very clear. Ho...

Q: Use the Divergence Theorem to compute the net outward flux of the field F=(2x, 3y, -z)  across the s...

A: To calculate the net outward flux of the given vector field across the given surface

Q: Logarithmic Differentiation - See attachment

A: Find the derivative of the given function.

Q: differentiate f(t) = t^(1/3)/ (t-3) On the solution guide on the first step for the numerator, we ha...

A: Explanation:Consider the term t1/3.It is known that adding and subtracting a same number to any numb...

Q: 3x2-3-4e2x and y(0) 8, then y= If dx x3- 3x - 4e2x x3- 3x - 2e2x + 8 x3- 3x - 2e2x x3- 3x - 2e2x + 1...

A: Click to see the answer

Q: 3x2-3 and y(0) = 8, then y(1) = If dx 4. 12. 0. 8 6.

A: As a first step, let\'s rearrange the term. Please see the white board. 

Q: Differentiate xy^2+tan(y^3)=10y

A: Consider the given expression:

Q: How can I get the result? Which is the result?

A: The given function is given by

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

A: (d) First draw the graph of y = x + 6 and y = x2.Find the intersection points as,

Q: The rate at which blood pressure decreases in the aorta of a normal adult after a hearbeat is dp/dt=...

A: It is given that rate at which the blood pressure decreases in the normal adult is dp/dt=–46.645e–0....

Q: please show ALL your steps

A: we are given a function 

Q: Find the domain: g(x) = ln(e^x -5)

A: The domain of ln z is z>0. We'll use the same concept here. So e^x-5>0. 

Q: How can I get the result? Which is the result?

A: We have to find following limits.Question is given below:

Q: dy If y 22 x, then dx 9.7 1. O 22 0. O 5. N O O O OO

A: The given equation is y=22+x.

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: 12. An oil tanker struck a reef and caused an oil spill in the ocean. Assume that in its early stage...

A: Let r be the radius of the oil spill which is circular in shape.Given, 

Q: lim x→-4   x2-16/x+4

A: The given function is f(x)=  (x2-16)/(x+4)The limit of the function is to be calculated

Q: The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be mo...

A: we are given a function  

Q: 2.5 Continuity 3. We would like to find a value of k to make the piecewise function f(x) continuous ...

A: 3)Answer: a) If I was to graph f(x) then the left part of 3 is changed when k is changed. As the k i...

Q: How do I show the correct solution for the differential equation? I know the answer is D.

A: First we separate the variables 

Q: The revenue from the sale of a product is, in dollars, R = 1500x + 3000(3x + 3)−1 − 1000 where x i...

A: The revenue from the sale of a product is, in dollars,R = 1500x + 3000(3x + 3)−1 − 1000where x is th...

Q: find the exact length of the curve of the equation in the picture below make sure to show all work

A: The given curve equation is,

Q: Calculate the area, in square units, bounded by g(x)=4x+8 and f(x)=x2 +19x+62 over the interval [−9,...

A: We have to find area between f(x) and g(x) for given boundaries.f(x) and g(x) is given below:Graph  ...

Transcribed Image Text

3 7. Find the second partial derivatives for f(x,y)=2x2y + 5y-3x'y 8. Find the total differential for z=-3ycosx+4x3y2 9. Let w-xy* - y, x-In t, y-cos t. Use Chain Rule to find dw/dt when t=0. 10. Find dy/dx implicitly for y5- y4 +3y+x3-6=0. 11. Find a directional derivative for f(x,y)-2+ x2 y2 at (-2,3) in the direction 6 of u cosi sinj 6 12. Find the gradient for f(x,y)=x2y-x In y at (4,1).