4. Use the theorem in Sec. 24 to show that each of these functions is differentiable in the indicated domain of definition, and also to find f'(z): (a) f(z) = 1/z4 (z #0); (b) ƒ(z) = e¯º cos(In r) +i e¯º sin(lnr) (r > 0, 0 < 0 < 2π). Ans. (b) f'(z) = i f(z) Z

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A: We need to find derivative.

Q: 2. Find the derivative of the following functions and write the down the inner and outer functions…

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Q: nd the points at which f(x) = cos² x has a horizontal tangent line. %3D

A:

Q: The derivative of: y =0( sin (In (0))) in (In (0))) + cos(ln (0)) is is:

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A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 3. (a) Let f be differentiable on an open interval I and suppose f"(x) = 0 for every x in 1. Show…

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Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition