7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

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

A:

Q: Moreover, suppose F(x) = f(g(x)) and G(x) = g(f(x)). Use the chain rule to calculate the following…

A: f(x)=cot x  and  g(x)=5x-2

Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

A: ANSWER :

Q: What is the first derivative of the following function: f(x) = (x³ + 2)4 O f'(x) = 12x²(x³ + 2)³ O…

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Q: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: Suppose that functions ƒ(x) and g(x) and their first derivativeshave the following values at x = 0…

A:

Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

A:

Q: 23 The derivative of the function f(x) = xª + is 23 4x3 (x²) 23 4x3 + (w³) 23 4x3 + (x) 1 4x 23 O 4x…

A:

Q: # 22 The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an ry X…

A: The probability distribution function is f(x)=21-1x2; for 1≤x≤2 and 0 otherwise. So in the graph of…

Q: 1. Find the derivative of the following functions at an arbitrary point x: 8 a. f(x) = x3/2 b. f(x)…

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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: 4. Suppose that f(4)= 2, g(4)=5, f'(4)=6, and g'(4)=-3. Find derivative h'(4) in (a) - (d). (a)…

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Q: The function g(x) = ln(x³ – 1) defined on V2, 0) is not zero unless x 2.

A: Given statement

Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+ 1)

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Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

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Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

A:

Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.

A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=3.

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x2 + 5x…

A: This is a limit and continuity problem

Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Answer

Q: e +1 Differentiate the function f(x)= In 5x +1 Se+1 3ex+1 Sesz e3x +1 ,5x +1 e 3e3z Sesz e3x +1 5x…

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Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

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Q: Compute the derivative function f' (x) algebraically. f (x) = –x² – 2x O f' (x) = 2x – 2 O f' (x) =…

A: Derivative of xn= nxn-1

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

A:

Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

A:

Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x>3 now show that it is continuous at x=3 or not.…

Q: 6. Find the derivative for each function. b. f(x) In 5x3 2)3 f(x) (e*3 2) а.

A: Use exponent rule for exponent 3 and use chain rule for (e^x^3 +2)

Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

A:

Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

Q: Find the derivative of the function. x+6 g(x)=| x2 +4 5(4 – 12x +x?) ( 6+x (4 +x²) a. g'(x)= 4+x?…

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Q: h) f(x) = ln (xe³z)

A: We will use the chain rule of differentiation and the product rule of differentiation to…

Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate

Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

A:

Q: The derivative of the function y = In (* + 1) (* - 1) is O y = O y = :- - 1 e+1 + -2 +1 ||

A: Question is solved.

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 3 5. h(x) x+5 = x2-9, 6. A(x) = v3x³…

A:

Q: Consider the function g (x) = x3, on the restricted domain [-8, 8]. Which of the following is the…

A: Explained below

Q: Suppose that functions ƒ(x) and g(x) and their first derivativeshave the following values at x = 0…

A:

Q: 1 4. Use the definition of the derivative to compute f'(x) given f(x) = 2x 3

A: Given,          The function is fx=12x-3 .

Q: Suppose 8 (x) = V x²+1, What is the correct result of the second derivative of g with respect to x?…

A: The function is given by gx = x2+1 To evaluate: The expression of g''x.

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x* + 5x…

A:

Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: to find:- first derivative of g(x), i.e. g'(x). *formula:- d/dx {e^x} = e^x d/dx {x^n} = n*x^{n-1}

Q: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…

A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…

Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

A:

Q: Find f'(x) (the derivative of f(x)) if f(x) = 7x'3 - 2x'2 + 4x - %3D 5. O 21x^2 - 4x + 4 + C O 21x^2…

A: