Find the gradients of the following functions 1. $f_1(x, y, z) = x^4 + y^4 + z^4 + xyz$ 2. $f_2(x, y) = e^x \cos(x + y)$ 3. $f_3(x, y) = \sqrt{1 + x^2 + y^2}$
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- ∂f1/∂x: derivative of x^4 is 4x^3; y^4 and z^4 are constant w.r.t x; derivative of xyz w.r.t x is yz. So ∂f1/∂x = 4x^3 + yz. - ∂f1/∂y: derivative of y^4 is 4y^3; derivative of xyz w.r.t y is xz. So ∂f1/∂y = 4y^3 + xz. - ∂f1/∂z: derivative of z^4 is 4z^3; Show more…
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Find the gradients of the following functions: (a) $f(x, y, z)=x^{2}+y^{3}+z^{4}$. (b) $f(x, y, z)=x^{2} y^{3} z^{4}$. (c) $f(x, y, z)=e^{x} \sin (y) \ln (z)$.
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