Question

Compute $f_x(x, y, z)$, $f_y(x, y, z)$, and $f_z(x, y, z)$ of the following functions: (a) $f(x, y, z) = e^{xz} + \frac{xy}{z}$, (b) $f(x, y, z) = x^2yz^2 - 4\cos(yz)$, (c) $f(x, y, z) = e^{xz} + y\ln(\frac{y}{x})$.

          Compute $f_x(x, y, z)$, $f_y(x, y, z)$, and $f_z(x, y, z)$ of the following functions:
(a) $f(x, y, z) = e^{xz} + \frac{xy}{z}$,
(b) $f(x, y, z) = x^2yz^2 - 4\cos(yz)$,
(c) $f(x, y, z) = e^{xz} + y\ln(\frac{y}{x})$.

Compute fx(x, y, z), fy(x, y, z), and fz(x, y, z) of the following functions:
(a) f(x, y, z) = e^xz + (xy)/(z),
(b) f(x, y, z) = x^2yz^2 - 4cos(yz),
(c) f(x, y, z) = e^xz + yln((y)/(x)).

Added by Jacob W.

Calculus: Early Transcendentals

James Stewart 8th Edition

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a) To compute f(x,y), we substitute the given values of x and y into the function: f(x,y) = 2e^x + b^f(x,y) - 2x^2yz^2 - 4cos(y) So, f(x,y) = 2e^x + b^(2e^x + b^f(x,y) - 2x^2yz^2 - 4cos(y)) - 2x^2yz^2 - 4cos(y) Show more…

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Compute f(x,y) and f(x,z) of the following functions: a) f(x,y) = 2e^x + b^f(x,y) - 2x^2yz^2 - 4cos(y) b) f(x,z) = e^y + 1/n

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