Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of some function on [a, b] ? Give reasons for your answer.

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

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Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: Is the function f(2) = -2(xy+x)+i(x² – 2y – y) differentiable? If it is, find it's derivative.

A: Consider the given function.

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

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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: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: Find the derivative of the following function F(x) = (2t – 1)³ dt using the Fundamental Theorem of…

A: Here I am attaching image so that you understand each and every steps.

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: Find the derivative of y with respect to x, t, or 0, as appropriate. y=x" In x - O A. 4x-x O B. x*…

A: The function is given as y=x4 ln(x)-13x3 Differentiate the above function w.r.t 'x' y'x=ddxx4…

Q: 13. Find the derivative of y = in terms of f, g, h, f', g' and h', where f, g, and h are functions…

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Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True 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: 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: Let f(x, y) = V xy. Find the derivative of f. af 1 ду 2

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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: Find the derivative at the given point. f(x)= at x = 0 %3D x+1 O 1/4 O-1

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Q: Why is the derivative of f(x) = e^2, 0? Would e to any power be 0?

A: Given f(x)=e2As the given function is in terms of x and the given function e2 is a constant

Q: Find the derivative of the function.

A: Some important derivative formulas: 1. d(lnx)/dx = 1/x 2. d(√x)/dx = 1/(2√x) 3. d[N/D]/dx = [D*(N)'…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). h(x)=…

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

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

Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

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: Find the derivative of the following function F(x) (2t – 1)³ dt X3 using the Fundamental Theorem of…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

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Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

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Q: Let y be a function of x and suppose y=In(x²+y²). What is the correct result for the derivative of y…

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Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: 3 Find the derivative of the inverse of f(x) = x +1 using the formula dy %3D 1 off "(x)= g'(x)= dx…

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

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Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: f(x) = e*

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Q: Find the derivative of the following function F(x) = / e (2t – 1)³ dt x5 using the Fundamental…

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Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: Find the derivative of the following function F(x) = (2t – 1)3 dt using the Fundamental Theorem of…

A: SOLUTION-

Q: Find the derivative of the following function F(x) = (2t – 1) dt using the Fundamental Theorem of…

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Q: The fundamental theorem of calculus says that the integral of the derivative of a function is the L…

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Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

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Q: Find the derivative of the following function 1 F(x) ds Va 5+7s4 using the appropriate form of the…

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Q: Suppose the derivative of f exists, and assume that f(2) = 1, and f'(2) = 2. Let g(x) = x2f(x), and…

A: Apply the product rule to find the derivative of g(x) and then substitute the given values as…

Q: Find the derivative of the following function. ° 4x y = In x y' =O %3D

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Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

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: 2. Find the derivative of h with respect to u if h = n²u

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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: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

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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

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: