117. Let F(x) = x/x2 – 1– 2 Prove that F(x) and y = cosh-x differ by a constant by showing that they have the same derivative. Then prove they are equal by evaluating both at x = 1.

Q: Prove that the function ax+b cx+d f(x)=- is constant (takes the same value for every x such that…

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Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: Use definition to find derivative of the following function at z = 3 – 2i.

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Q: Let f (x) = x² – 3. a) Use the definition of derivative to find f' (x).I (Write your answer in the…

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Q: (g) Suppose the first derivative of f(x) is f'(z) = z - 62 + 11z – 6. Where is f(z) increasing? Use…

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Q: 2. Let f be defined by { x 0. f(x):= I 0 Using the definition of the derivative, verify if f has a…

A: We need to find derivative.

Q: Let z = a + ib and f(x) = exp (zæ), then find the 1st and 2nd derivative of f(x).

A: Given: f(x)=ezxwhere,z=a+ib

Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

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Q: 2.2 Use the Cauchy-Riemann equation to determine if the function f(2) =r- i(2-y)" is analytic or…

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Q: 9. Use the definition of derivative to find the derivative of f(x) = x² – 3x.

A: We need to evaluate the derivative of the function f(x) using definition of the following function…

Q: 9. Let f(x) = cos 2x. Calculate f(50) (x), the 50th derivative of f(x).

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Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find the second derivative of the following function at x = 2 y = (x +) 2 G+x)

A: Given function is y=x+1x2

Q: 1. Let f(x)=√x-2 / x-4 . Show that f(x) has a removablediscotuiti t x=4   2. Given f(x)= √(x+1).…

A: Here we have to find the derivative of a function at a point.

Q: f(x) = 4√x + 2x1/2 – 8x-7/8 + x2 1 23 +2

A: The given function is fx=4x+2x12-8x-78+x2-1x3+2. Find the derivative of the given function. Here we…

Q: 6. Use the definition of the derivative to show that the function f(z) = Z is nowhere…

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Q: 3. Use the formula ((x+h)-f(x) to approximate the derivative of f(x) = 3x² at x = 1 h using h = 0.1.…

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Q: Let g(u)= √8u+- 4 Determine the derivative of g. dg

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Q: The sign x (t) is even symmetric and the sign y (t) is equal to the derivative of x (t). Show that…

A: even symmetric means it satisfies x(t)= x(-t) while odd symmetric means it satisfies x(-t)= -x(t)

Q: 5. Compute the derivative of f(x) - x³ (x-7) tan(x) √1-x (You do not have to simplify your answer.)

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Q: 7 x = R¹, ƒ(x):=· + 3√x² 1-x 1+x² +ea² +1 +π².

A: The power rule of differntiation states that d dxxp=pxp-1, where p is any real number. The quotient…

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)