If the derivative of the function is zero everywhere, the function is always O a. variable O b. None of these O c variable + constant O d. Constant State the interval of the function f(x) = V3 – x is continuous a) (-0,3] b) [3. ) c) [3.0] d) None of thes O a O d O b

Q: Find the derivative of y given that y= x In x to ex A None of the given choices 1-In x-x In x B ex…

A: We can find the answer as below.

Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x =1, assuming…

A: Given, f(1)=4, f'(1)=-1 y=4xf(x) y'=(4xf(x))' =>y'=4(xf(x))'

Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

Q: By considering the derivative of the function f: [-1,1] → R defined by f(r) = show r2 +1' that f-1…

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Q: Determine the derivative of the following function: f(x) = 3ecos(3x) cos(3 x) O 9e cos(3 x) O…

A: f(x) =3ecos3x differentiating function with respect to x

Q: Compute the derivative function f'(x) algebraically. f (x) = 3x2 +x lima 0 (6z + 3h + 1) = 1 limp 0…

A: Given Data: Function: f(x)=3x2+x For f(x+h), Substitute x+h for x in the given function.…

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: 5. By considering the derivative of the function f : [-1,-1] → R defined by f(x) = show that f-¹…

A: Concept: inverse function: An inverse function, sometimes known as an anti function, is a function…

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: . Show that the following function is differentiable everywhere on R but of which the derivative is…

A:

Q: 1. (x*+2x)°(6x²+4)dx 2. [3x²+2x+1 dx 3. (x?)/(x³-4) dx 4. (x+1)/(\x²+2x+1) dx

A: As per the guidelines we can solve 3 problems only.

Q: Let a be a real valued constant. Find the derivative with respect to x: y = 1-4ae4x O y (x) = 16ae…

A: The solution is given below in the next step:

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

A: As we know that the derivative of uv form is given by ddxuv=u'v-uv'v2 see below the answer and…

Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let f(x) be a function that is differentiable at x = -2. Given that f'(-2) = 3 and f(-2) = 6, find…

A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

Q: Suppose that f is a differentiable function with f(2)=5. If the tangent line to the graph of y= f(x)…

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Q: 2. Let f : R → R be a differentiable function. Show that the function f', the derivative function of…

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Q: If a function is defined by an equation G(x,y)=0 and could be found explicitly as y=f(x), then the…

A: We have to check

Q: Let y = f(x) be a differentiable function. If the derivative of f is zero at x = a, then the…

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Q: 33. The line y = 2x - 6 is tangent to the graph of the twice-differentiable function f at the point…

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Q: Give a value for c that satisfies the conclusion of the Mean Value Theorem for Derivatives for the…

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Q: If f(x) is odd function, then the derivative of y =sinh (-x)) equals Select one: f'(x) O y'=- V…

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Q: Starting from the definition of derivative prove that if f(x) = 1 then f'(a) = a2

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Q: If F(x) is a differentiable function with derivative F'(x)= Enx"-1 and F(0)=0, then F n=2 x2-x O 1-x…

A: Introduction: For a differentiable function fx, if f'x is given, then integrating both sides, fx can…

Q: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

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Q: 3. If f(-1) = 3, f'(-1) = 5, g(-1) = -1, gʻ(-1) = 2, let h(x) = f(x) g(x). Find an equation for the…

A: given: f(-1)=3, f'(-1)=5, g(-1)=-1 and g'(-1)=2 h(x)=f(x)g(x). we have to find the equation of the…

Q: Determine the points in the interval [0, 2π) at which the graph of the function f(x) = √2x + 2…

A: We find point of tangent on given curve.

Q: 4. Find the second derivative of each of the following and determine based on your results if the…

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Q: 20 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph…

A: We have to find

Q: HW prove That The derivative of Flx)=x-x is if (x) = 3x?1 use definition of devivativeto finid The…

A: Use following mentioned rules to find the derivative of the function. The power rule of…

Q: 6. If fand g are two differentiable functions at x, then 7. The derivative of the identity function…

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Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x = 3, assuming…

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Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: Solution :1.fx=23x3-2xfirst derivative ,f'xf'x=29x2-2Second derivative…

Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan…

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 +…

Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x = 3, assuming…

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Q: At what other point does the tangent line drawn to the curve f (x) = x ^ 3 from (2,8) intersect?

A: Given curve is : f(x)=x3   ..............(1)           and tangent drawn from (2,8)

Q: (a) Find the derivative of y = f(x) =2x+1 using this definition f (x+h)-f(x) f'(x)= lim h (b) If x…

A: Differentiate above function with respect to x

Q: If f(x) is odd function , then the derivative of y =cosh-1(f(-x)) equals Select one: 1 o y'= -…

A:

Q: FIND THE DERIVATIVE OF THE FUNCTION DESCRIBED. (25 1. y (x2- 1) (2x+1) 2. y 2x2 (4x² + 3x- 5) 3 y +1…

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Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Show that the function f(z) does not admit an anti-derivative in the domain N = C\{0}. Does it admit…

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Q: Let the function y(x) be given implicitly via the equation xy – In y = 2. Determine the value of its…

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Q: The derivative of the function f is given by ƒ'(x): = e¯* cos(x²), for all real numbers x. What is…

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Q: 3 if x 2 the one-sided derivatives of f at x = 2 whether f' (2) exists. If it exists, specify its…

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Q: The function f (z) = |z|2 – ī is differentiable at a single point in C. Find that point and prove…

A: Given function is fz=z2−z¯ We have to check the function where it differentiable. It is enough to…

Q: 2.r By considering the derivative of the function f: [-1,1] → R defined by f(x) = show r2 +1' that…

A:

Q: suppose the derivative of f exists, and assume that f(2)=3, f'(2)=4. Let g(x)=x^2f(x) and h(x)=…

A: The objective is to find the equation of tangent lines of g(x) and h(x) at x=2