Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only differentiable at z = 0 and find the value of f'(0).

Q: Determine the directional derivative of f(x, y) = 3x² + [y] at the point P(-1, -1) along the…

A: Explanation of the answer is as follows

Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: Consider (x, y, z) = 4xy²+ 3y sin(z) and at the point P = (1,2,0) calculate the directions in which…

A: Approach to solving the question:To find the directions in which the…

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eu + cos(v)). Use…

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Q: Prob3: Find the derivative of the function at P, in the direction of A f(x,y,z) = (1.0.). = cos xy +…

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Q: Find the direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

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Q: (a) Let f(x,y) = x² – 5xy. (i) Find the directional derivative at (2, 1) in the direction of i = -i…

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Q: QI/Find the derivative of the function f(z, k) = z* – 16k³ + tanh(z) – 4 csc(k) in terms of z and k…

A: F is the function of two variables so we have to calculate partial derivatives