ectional derivative of f at the given point in the direction indicated by the f(х, у) — sin(x + 2y), (4, –2), 0= 3™/4

Q: Determine the derivative with respect to t x = tcos^2(2t^2 - t)

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Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

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Q: Find the derivative of f : R³ → R² defined by f(x, y, z) = (-3x²y, e-3y-2:). The derivative f' : IR³…

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

Q: Find the derivative of the function at Po in the direction of A. f(x.y,z) = xy + yz + zx,…

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Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x, y) = 10xye-(x²…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx,…

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Q: The directional derivative of fhe finction f(x, y, z) =x²z+ xyz + y² in the direction of u-2i +j-k…

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Q: 1-Vx Let f (x) = Which one is the derivative of f (x)? = COS 1+vx

A: Solution: The objective is to find the derivative of the given function

Q: a) Prove that (arctan r 1+2 b) Using part(a), find the derivative of f (x)= arctan (208 )

A: Properties of derivative  f(g(x))=f'(g(x)) g'(x)ddxcosx=-sinxddxax=axloga

Q: -2 (a) Show that f'(x) using the definition of the derivative. (2x + 7)² (b) Find the equation of…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx, Po(1, - 1,…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx, Po(3, - 3,…

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Q: What is the second derivative of f (x) =csch¬'(tan(x))? A f"(x)=- sec2(x) B) None of the given…

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Q: 3. Use the second derivative test to find the local extrema of f(x) = cos x + sin x on the interval…

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Q: a) Find the first derivative of the followings: i) f(x) = sec²x tan/x ii) f(u) = cos²(sin(1 – u)-1)…

A: We have to find out the derivative

Q: Using the definition, find the derivative of f(z) = 3 z4-6 z? at point z= 0

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Q: f(r+h)-f(x) Using f'(x) = lim Find the derivative of f(x) COS T.

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Q: estion 9 Find the derivative of f(z) = 3z13 - 4+1. IDo? la sin (a) f' (x) =}

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Q: Using the definition, find the derivative of f(z) = 3 z4-6 z at point z= 0

A: The derivative of the function f(x) is given by f'x=limh→0fx+h-fxh. The given function is…

Q: Find the derivative of the function at Po in the direction of u. x-y g(x,y) = Зху +2. Po(- 1,1), u=…

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Q: ! The derivative with respect to x of the function sec y where y = sec ¹ (2* cot¹x) is sec(2* cot¯¹…

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Q: Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not…

A: We have to find  an equation of the tangent line to the graph of the function f through the point…

Q: Find the derivative of the function at Po in the direction of u. X- y g(x,y) = Po(- 1,1), u= 12i +…

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Q: Evaluate the derivative a. h(x)= (sin x + 2cos x)^1/2

A: The given function is hx=sinx+2cosx12.

Q: Find the directional derivative of f at the point P in the direction of a. i-j f (x, y) = 2x3 – 6y³;…

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Q: suppose u and v are differentiable functions of x. Use the given values o fthe functions and their…

A: Consider the given information: u2=6u'2=2v2=-3v'2=-4 Consider the given derivative. ddxuvx=2

Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

Q: Use chain rule to find the derivative of the function below: y = cot(t –) -10 y = E- 10) y = tan(5 –…

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Q: a) Find the first derivative of the followings: i) f (x) = sec²x tan/x ii) f (u) = cos²(sin(1 –…

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

Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6, 8) is 14 O…

A: Here,

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x,y) =…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = - 3 ex cos (yz),…

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Q: The directional derivative of the function f (x, y, z) = x²z+ xyz + y? in the direction of u = 2i +…

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Q: The directional derivative of the function function = x - xyz + y? at the point (1, 2, -1) in the…

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Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

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Q: e derivative of f(x) = 6. (x² + 15x) is | O -6x 3(2x + 15) O 6x + 90- O -6x 2(2x + 15) O 6x 2(2x +…

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: We have to find directional derivative of f at a given point.

Q: Construct a table of values for cosx, x = 0,0.1, 0.2, ..., 0.6. Using the difference quotient,…

A: We know that  cos0=1, -sin(0)=0 Here, we use difference quotient. We have…

Q: Consider the function f(x) = 3cos(2x). (a) Find the derivative of f(x). (b) Verify that the…

A: (a) Given function is f(x)=3cos(2x) The derivative, f'(x)=-6sin(2x)

Q: Consider the function f (x) = 212 + 12e. a) What is the derivative of f at z 0? f'(0) = Number b)…

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: State De-Moivre's theorem. Compute n" derivative of the function y th x² +a?

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the derivative of the function at Po in the direction of A. f(x,y) - - 3ху + 5y, Po(1, - 5), А-…

A: We have to find the directional derivative of the function P at (1,-5).

Q: F(x,y) = In x+y of the function at the point %3D P( 3,4) ond V= [ = -7+ 2 find the derivative %3D in…

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Q: 5. (а) Find the directional derivative of f at P in the direction of ā if f(x,y) = y In(x) ; P(1,4);…

A: To find The directional derivative of f at p in the direction of a.

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Q: Find the directional derivative of the function at point P in the direction of Q. f(x, у, z) P(2, 1,…

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Q: b) In general, what is the derivative – 2) = Check your answer from a) by means of classic rules of…

A: We have to find derivative

Q: Q:4) Find the directional derivative of the function f(x.y,z)-x²+y*+z°-2 at the point po(1,1,1).

A: here we are not given the vector in whose direction we need to find the directional derivative so…