(a) Calculate the differential df of the function f = tan(x). Use it to find an = π/4, approximation for the change of f in the vicinity of x i.e. ▲ƒ = f(x) − f(7/4), in the form of differential df at x = π/4. (b) Use this differential to approximate tan(π/3) given that = П +聶 .

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Given the function fx)=x cosx. Use the centered-divided-difference formula f '(x) = 2h to compute…

A: We will use center difference formula  f'(x)=f(x+h)-f(x-h)2h

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A: Introduction: The four-step method to find derivatives is actually determining the derivative of a…

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A:

Q: 11. Estimate the approximate derivative of f(x) = sin²(x) at x = 0.45 radian, for h = 0.05 and 0.1…

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Q: f(t)=5 sec²(7 Tt – 3)

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Q: a.) f(x) = sec(e") b.) g(x) = tan¯'(x)+3* +x!5 %3D _1.5

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Q: Find f'(t) and simplify your answer. cost f(t) = 1 - 2 sint

A: Given function is a quotient function and we proceed with finding the derivative of f/g…

Q: Let f (x) = 4 tan (7x). Find the values of the coefficients in the expressions for f' (x) and f"(x)…

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Q: 2+ cosh r (r² + 4) Compute the derivative of y = In I - (r+ 1) Compute the derivative of f(x) =…

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Q: Find the derivative of the function y = sinz Select one: 2rcosz-r sinz a. cos?r 2xcosz+z sinz cos z…

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Q: Find the derivative of r = In (cos" x).

A:

Q: Consider the function f(x) = 4 sin(x) cos(x) + 6 csc(x). Evaluate its derivative at the point x =…

A: Product rule of derivative is used.

Q: The forward difference approximation to the derivative f(x) = x² sin(2x) at x = π/3 is: (use step…

A: The forward difference approximation to the derivative f(x) = x2 * sin(2x) at x= π/3 (use step size…

Q: A2) Find the derivative of the following functions: x2 + 2 (a). f(x) x2 – 2 (b). f(x) = 2 tan-1(x) –…

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Q: O Find the derivative of the following functions: L 2+3 (a). f(z) = 2-3 (b). f(z) = 2 tan (z) – 7…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (a). Find the derivative of f(x) = 4 sin x + x² cos x. (2 Marks) %3D (b). The position of a particle…

A: Follow the steps.

Q: The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)

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Q: Find the first and the second derivatives of the function where a is a parameter (1.e. a real…

A: fx=eax-e-axxeax⇒fx=eax·xeax-e-ax·xeax⇒fx=eax+ax·x-e-ax+ax·x⇒fx=e2ax·x-e0·x⇒fx=xe2ax-x Now…