2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say about the concavity of F?

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A: Leibnitz integral rule.

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A: The resulting change in function f (x, y) is given as:

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A: Answer

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A: y=uxvx, where ux  &  vx are the differential functions of x. To differentiate these type of…

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A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

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Q: I need help with this question

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A: We use the exponent rule and chain rule.

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A:

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A: We have to find

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

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

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A: Topic : differentiation

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A: Given :                xy = 3  , dydt = 4 To find :                      dxdt when x=2

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

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Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Suppose that x and y are both differentiable functions of t and are related by the given equation…

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A: Integral calculus is one of the two main parts of calculus that is concerned with the study of…

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A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

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A: Solution:-

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A: (a) Trapezoidal Rule. First we need to find the maximum of f''x. In the problem given, fx=7x.…

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Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

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Q: Does the differential dy represent the change in f or the change inthe linear approximation to f ?…

A: Given the differential is dy.

Q: Q /Choose the appropriate derivative for this function y = (x+ 1)2* dy = 2* (x + 1)2" - In(x + 1) dx…

A: Explanation of the answer is as follows

Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: 2. About what point is the local linear approximation l(x) 1 of the function f(x) = tan- x 4 valid?

A: Let's Solve,

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

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A: We will find an example

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Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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Q: Find the values of x on [0, 2 ) π where the tangent line of f x( ) be horizontal. y=e^-x (cosx)

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Q: The Derivative az/ax of sin(xy+z)-sin(zx- * :y)+sin(yz+x)=1 is -ycos(xy+z)-zcos(zx-y)-cos(yz+x)…

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Q: b)x > 0 impending all continuous f function | f(t)dt = x. arctan(x) f(1) =?

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Q: The derivative of y=eev* +cosh x equals Select one: O y' =eev +sinh 2/x 「Oy=SeV全 + sinhx 2/x ev…

A: Given: y=eex+coshx To calculate: Derivative of y