1 1. The function Y = sin(t² )+ 4 is graphed below. Define F(x) = [, sin(1²) + - 1 dt 4

Q: Let f(x) = -2 ln(cos(x)) f''(x) =

A: dlnxdx=1xdcosxdx=-sinxdtanxdx=sec2xsinx cosx=tanx

Q: 5. Consider the function f(x). f(x) = (2x² + 3x + 1 |x| sin(x - 1) + 1 if x < -1 if -1 < x < 1 if 1…

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Q: x3 C. g(x) : et

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Q: The derivative F' (t) is graphed in the figure below. Given that F (0) = 12, calculate F(t) for t =…

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Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

Q: b) Find the points at which the function f: C → C defined as: f(x + yi) = x - yi Have a complex…

A: To find the points at which the function f(x + yi) = x - yi has a complex derivative, we need to…

Q: 1. þompute and simplify the derivative with respect to x for each of the following functions: a)…

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Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

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Q: 3) Find the following derivatives: a. y = 2x b. f(x) = 4x³10x² + 7x-15 c. g(x) = 3x(x² - 4)5 d. y =…

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Q: 1. a) Copy and complete the table below: Original Function First derivative Second Derivative y =…

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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)