Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

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 slope of the line tagent to the curve of y = In x/x at point (1,0)

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Q: Find derivative of 2x^4y^3-xy^2 using chain rule.

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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 derivative of the function f(x) = 2sin x %3D

A: Given       f(x)=2sin x

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

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Q: as y y = f(x) (10, 4) Tangent line (4, 2) ive your answer to three decimal places.)

A: G

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

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Q: What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point…

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Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

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Q: The total derivative of f(x,y) = ylnx  is

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Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - -2, and the line 4…

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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: 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: Find the derivatives of the functions in Exercis

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

Q: Find the maximum rate of change of f at the given point and the direction in which it occur f(x, y)…

A: Topic- Vectro

Q: can explain for me what is Applications of Partial Derivative ?

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Q: By using quotient rule, differentiate f(x) = (2x* – 7x² + 3x)(x² + 1)-1. Hence, find the gradient of…

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Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

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Q: Determine the directional derivative of X²Yz +4XZ² at the point P(1,-2,1) in direction a=2û - j +² R…

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Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

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Q: Suppose that f(x, y) = xy. The directional derivative of f(x, y) in the directional and at the…

A: Explanation of the solution is given below....

Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional and at the…

A: we will find the directional derivative

Q: Suppose that f(x, y) = x°y. The directional derivative of f(x, y) in the directional (– 2, – 1) and…

A: Explained below

Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (- 3, 1) and…

A: First find gradient at point and take dot product with unit vector

Q: Еxample 5 1 1- Vxdx ха 0,

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Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

A:

Q: Find the derivativeof the following function:

A: To determine derivative of the function.

Q: Find the derivative of f(z) = (x³ + 5)(z³ – 5) %3D (8z")(5x*) (8z +5)(z – 5) + (z³ + 5)(5x* – 5) (8z…

A: We need to use the product rule.

Q: 1, cosX, cos 2X,--- , cos mx

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Q: Find an equation of the tangent line to the curve y = 2x2 + 3 that is parallel to the line 8x – y+ 3…

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Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: Evaluate the required second order partial derivative. Find fxy(5,-1), if f(x,y)= -2xe5y

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Q: 5z²)* 4/3 %3D

A: (3). The function is given by Hz = 1-5z243 To evaluate: The derivative of the function.

Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f…

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Q: Give one problem for  partial differentiation of function of U with respect to 3 independent…

A: It is partial derivative problem

Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

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: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2

Q: Find the area bounded by the curve 4 square units 8 square units 16 square units 10 square units =…

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Q: Let f(x,y) = x^2 y + e^xy sin y.   At Point (1,0) State the direction where the function…

A: Given: fx,y=x2y+exysiny