What is the fxx, fyy, and fxy of f=(2x^4)+(y^2)-(x^2)-(2y)?

Q: Compute the derivative using derivative rules that have been introduced so far y = (4 - 2x - 3x 2) 5

A: Given: y=4-2x-3x25  ……1

Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

A:

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Find the second derivative of the funcion. y%3D

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Q: Find the orthogonal trajectories for the family of curves 6x² + y² -9ax=0.

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Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Verify by differentiation that x4 is an antiderivative of 4x3.

A:

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: Use implicit differentiation to find az/əx and az/ðy. x² + 4y2 + 5z2 = 4

A: Given

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

A:

Q: Find the derivative of the function. y = x 5 Vx3+7 O y'=- 2VX3+7 3x7 5x3 Vx3 +7 3x6 O y'=. 5x4 Vx3…

A:

Q: What function should be used to minimize the distance between, y = 3x2, and the point (0, 2)?

A: y=3x2,  0, 2.

Q: Use implicit differentiation to find zx x6y5-x4tan z + 2y2z3 = 7

A:

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the orthogonal trajectories for the family of curves y=c1x4

A: First of all rearrange the given equation in such a way that both the variables be on one side of…

Q: dy Use implicit differentiation to find dr 4x²+ 6ln(xy) =9 y(4x²+ 3) а. 3x 4x²y b. 3 - с. Зу y(4x²–…

A: Solve the following

Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the curve in the xy-plane that passes through the point (9,4) and whose slope at each point is…

A:

Q: Find the derivative of f(x) = (1 + 7x2)(x − x2) in two ways. 1. Product Rule 2.Perform the…

A: For product rule we use u=1+7x^2 and v=x-x^2Product rule = u'v+uv'Answer: f'(x)=1-2x+21x^2-28x^3

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: at the line x = 3. %3D

A: Find the volume of the solid generated by revolving the region between the parabola  x=y2+1 and the…

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Find anti derivative of 4cscxcotx + 3/(sqrt(1-x2) - 1/(cubrt(x5)

A:

Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

A:

Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: ) Find the equation of the tangent f (x) = 4x - 8/x at a = 16. %3D %3D

A: Given: fx=4x-8x at x=16 For finding equation of tangent at x=16, we need to find y-coordinate for…

Q: Find the point on the parabola y= -X-+4 whose tangent line is parallel with y= 3x-5,

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Q: 1. у %3D 4x2 — 3х — 2.

A:

Q: Еxample 5 1 1- Vxdx ха 0,

A:

Q: 9. y = 3x – Vx

A:

Q: Find the derivative of f(x) = (2x^2-x-1)(sqrt of x) %3D

A: A detailed solution is given below.

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

A:

Q: Find all points on the curve 3x + 6y² = 36 where the tangent line also passes through the point (10,…

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Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

A:

Q: Find the slope of the tangent line of f (x) = 2x² - 3x + 2 at x = 2 %3D

A:

Q: 7. y = Vx + 2

A: Using Delta method differentiate y. And using rationalising.  Follow step 2nd  .

Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Find the points on the graph of f(x) = 36x – 3x³ where the tangent line is horizontal. %3D

A:

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: y 1-

A: The solution is given below in the next step:

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

A:

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.