If f is a differentiable function at a, then f2 is differentiable at a and (f2)'(a) is: Select one: O a. 2(f')²(a) ОБ. 2f(а) +2f' (а) O c. 2f(a)f'(a) O d. 2f(a) + 2f'(a)

Q: 2. Express in indicated derivative in terms of the function F(r). Assume that F is differentiable.…

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Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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Q: find the directional derivative of f at p in the direction of B.  if f(x,y,z)=x+ycos(z) where p…

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Q: 75. F(x) : (t + 2) dt

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Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

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Q: (b) A bounded, 3B > 0 such that |f(x)| < B Vx € (0,1), continuous function on (0,1) with unbounded…

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Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be…

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Q: x2 f (x) = t² sin(2t) dt 1

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Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x&gt;0…

Q: (a) Find the partial derivative of f with respect to x. fx(X, y) = (b) Find the partial derivative…

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Q: What does it mean for a function ƒ(x, y) to be differentiable? What does the Increment Theorem say…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: The implicit derivative formula on a surface F (x, y, :) = 0 is: *--() F Evaluate d:/Əx on the…

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Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in the…

Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: Use Caushy Reman equations to Show that ĕ (Z) anel its derivative f(Z) exist Verywhere and find ぐ(z)…

A: Given: fz=z3 Rewriting given function we get, fz=x+iy3fz=x3-3xy2+i3x2y-y3 Now comparing, it with…

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: The coordinates of a particle in the metric xy-plane are differentiable functions of time t with…

A: The distance of a point (x,y) and the origin is calculated by d=x2+y2 Given rate of change is,…

Q: The slope of the tangent line to the differentiable function f at the point (2, f(2)) is…

A: It is given that the slope of the tangent line to the differentiable function f at the point 2,f2 is…

Q: Find the tangent line approximation for f(x) = v2 – x at x = -2. Use it to estimate the value at x =…

A: Solving using linear approximation formula

Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

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Q: I. Show that the function ƒ defined by (1, y) = (1, –1) f(1, v) = { +g (z, y) # (1, –1) + y is not…

A: We will use the sequential characterization of continuity to solve this problem. The detailed…

Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

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Q: Find the maximum value of the directional derivative of the function f(x, y) = tan at the point…

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Q: sin(x+y) x+y (x.y) (0,0) F(x, y)={ 21 (x.y) (0.0)

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Q: What

A: The correct option is (B).

Q: Are there independent linear functions with derivative number n – 1 continuous 91 ,..., „,with…

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Q: Find the direction 0 in which the directional derivative of the function f(x, y) = æy+ y² at the…

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Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

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

A: We can solve this as follows:

Q: Suppose f and g are two differentiable functions such that f(9(x)) = x? and supposed the equation of…

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Q: By using caushy Rieman find the derivative of f(z) =Iz| if it exit ® fLz) = 2 +Z1

A: It is given that the function fz=z. The function fz=x2+y2. Note that, If the function is…

Q: 5. What is the value of the second-order derivative of the function with parametric expression x =…

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Q: ind the 9th derivative of f(z)=exp((-1 + isqrt 3)z) at z=0.

A: Given f(z)=e(-1+3)z Differentiating w.r.t 'z' f'(z)=e(-1+3)z(-1+i3) f''(z)=e(-1+3)z(-1+i3)2…

Q: 2) f(z) = (« + iy)“ - i (x+ iy)

A: Given function: fz=x+iy2-ix+iy.   We know that if fz=ux,y+ivx,y is analytic then f'z=ux+ivx=vy-iuy.…

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

A: It is partial derivative problem

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

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Q: ar Let = 2x - 1. Integrate this partial derivative with respect to x, letting h(y) be an unknown…

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Q: (a) (b) Explain the differentiability of f on R by using definition. Let f' be the first derivative…

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Q: /alue of divergence of function (x2y2)î - (z³y – 4x) ĵ + 4y2 xk at (1, 2, 1) is

A: Let f = (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: -2 In(x) Consider the function f(x, y) = 3y

A: We have to find the derivative of the function f(x,y) in the direction u=-5,2.…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.