Here is the graph of the derivative of a continuous function f: R → R. What would we see on the graph of f when x=0? f'(x) O A corner. A jump. O A cusp. O A vertical tangent A horizontal tangent.

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: The function f(r) = sinh(r) is one-to-one and so is invertible. Using our rule / formula for…

A: First I have written the relation between derivative of inverse function and original function ,…

Q: a. Find the derivative of f at x. That is, find f'(x). b. Find the slope of the tangent line to the…

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Q: The picture below shows the graph y = f'(x) of the derivative of a function y = f(x). For each of…

A: We have to classify the corresponding point on the graph of y=f(z) for each of the labelled points…

Q: Which of the following is the derivative of * f(x) = In(tanhz)? %3D

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Q: Find the Derivative of the given function. If f(t) = tan '(In(t")) . then f'(t) If g(t) = In(tan…

A: To find the derivative of the given functions we need to use chain rule of differentiation.…

Q: The derivative of a function f(x) at a particular value of x can be approximately calculated by f(x)…

A: The given function is f(x)=7e0.5x.

Q: Find the derivative of y with respect to x. 1 y=x' In (x)---x obra d we do O A. 7x5-x² OB. 8x5-x2…

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Q: ind the derivative with respect to x for the follo a. y = 43x b. f(x) = 22x3cos x c. y = tan(23*) d.…

A: Since you have posted multiple questions with multiple subparts, we will solve the first three…

Q: a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent…

A: Given: fx=x2-5x To Find: a. f'x=?b. Slope of tangent line of the given function at x=-1 and x=3

Q: The graph of a function is shown together with the tangent line at a point P. y 2 1 2 Estimate the…

A: According to given figure derivative of given function at point P is equal to slope of tangent Now,…

Q: Show that the function y=| × | is differentiable on (-o,0) and (O, c0) but has no derivative at x =…

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Q: Differentiate the following functions in derivative and differential forms: f,(x) = Ax f,(x) = In x…

A: For f1(x)=Ax ⇒f'1(x)=Adxdx⇒f'1(x)=A Sketch of f1(x)=Ax limx→∞A=A

Q: The function f whose derivative is f'x) = (x – 1)e"* is decreasing on (-00, 1). Select one: O True O…

A: We Know that the derivative of a function may be used to determine whether the function is…

Q: The function f(r) = tanh(r) is one-to-one and so is invertible. Using our rule/ formula for relating…

A: Given that

Q: If h =z-2, which of the following best describes the derivative of f at r /(z+h)-f(z) 1. lim 0 I.…

A: Given that h=z-x Derivative of f at x

Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A: From the left side of x=1, the derivative is

Q: Find the derivative of the given function. (²) w(x) = sin a) w'(x) = -cos COS ( 1 ) Obl wd-es() 1 b)…

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Q: Suppose In (x + 2y) = x*. Use implicit differentiation to find the derivative of y with respect to…

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Q: 8. Given that f(r) is continuous at r = 0, is f(r) differentiable at z = 0? (If yes, find f(0) using…

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Q: Here is the graph of the derivative of a continuous function f: R R. What would we see on the graph…

A: Given that a graph of the derivative of a continuous function f:R-->R.

Q: The function f(r) = sinh(r) is one-to-one and so is invertible. Using our rule / formula for…

A: When the inverse of a function y=fx is f-1x then the derivative of inverse is given by…

Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. Spx + 1, if x…

A: The limit of a function at a point is the value of the function when the variable is very close to…

Q: Define the derivative f'(a) of a function f at x =a.

A: To define: The derivative f'(a) of a function f(x) at x=a

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: Find the derivative of f(x)=e^c+c^x. Assume that c is a positive constant. f′(x)=

A: Consider the function  f(x)=ec+cx,       c>0

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

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Q: If the derivative of y = etanx is y' = m etan x, what is m? A. sec x tan x B. 1+ tan?x C. 1- tan?x…

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Q: Choose the right value of the following integral sie3f(=) f' (x) dx. where f is a continuous,…

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Q: 2) Suppose the graph of f (x) and the graph of its derivative f '(x) are shown below. Find an…

A: From the graph of f(x) , at x=1, f(x)=1 From the graph of f'(x), at x=1, f'(x)=-2

Q: For a function f, we define the ___________________________________, denoted f’, by…

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Q: Suppose g: IR - IR is a differentiable function with bounded derivative, Fix e> 0 , and define flx)…

A: to show f is one one we will show that for  x1 not equals to x2 , f(x1) is not f(x2)

Q: Let f(z) = z – 6z. Calculate the difference quotient (3+h)-{(3) - for h = .1 h = .01 h = -.01 h = -1…

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Q: What is the definition of the derivative of a function at a point? Are there real numbers a and b…

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Q: find the derivative of y with respect to the appropriatevariable. = (1 - t) coth-1 √t

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Q: Find the derivative of the following functions. (a) f(x) = tan(x) tanh(x) (b) g(x) = e** cosh(2æ)…

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Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: 2) Suppose the graph of f (x) and the graph of its derivative f'(x) are shown below. Find an…

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Q: Find the derivative(dy/dx) of following function f(x) = Sin(2x) (x+1)? %3D

A: It is derivative problem.

Q: 3. Calculate the derivative of the following functions. DO NOT SIMPLIFY a. f(x) = tan (In(x) +x² –…

A: Trigonometris identities d/dx(tanx)=sec2x d/dx(in(x))=1/x d/dx(xn)=nxn-1 d/dx(sinh(x))=coshx…

Q: Find the derivative of the function toy do not nad to Sumplity your answer y= e* In (2)

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Q: Let f(x) = The slope of the tangent line to the graph of f(x) at 33 - the point (8, 5) is The…

A: To find the slope and equation of the tangent line of f(x) at the point (8,5).

Q: Show that the following function is continuous at x = 1 for all values of p. (px + 1, if x > 1 f (x)…

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Q: Take the function (e 1>0 f(x) = %3D Compute its derivative at all values of x € R. Is f'(r) itself…

A: Given:   To determine: differentiation of f(x) and differentiability of f'(x)

Q: Consider the function defined by f (x) = -x + ae" where a E R: (1) find a such that the graph of the…

A: To Determine: Consider the function defined by f(x)=-x+aex-1 where a∈ℝ find a such that the graph of…

Q: Consider the derivative function g (x) = 3 cos (4x – 1). %3| What is the general antiderivative of…

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Q: Find the value of deriVative beloW 3 If x*y5 + x?y³ – xy² + 5y + (x²y+)² = x), then 3y'at(-1,2) = O…

A: derivarive of functions in product and using chain rule of differentition

Q: Find the first derivative of the function below: f(#) = cosh(cot(z² – 2x – 7)) %3D

A: