Find the gradients of the following functions: a) f(x.y,z) = x2 + y3+z4 b) f(x,y,z) =...

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Find the gradients of the following functions: (a) f(x, y, z) = x2 + y3 + z4. (b) f(x, y, z) = x2y3z4. (c) f(x, y, z) = ex sin(y) ln (z).
x + y + z = 5 x + y - 4z = 10 - 4x + y + z = 0 Solve the system by inverting the coefficient matrix and using Theorem 1.6.2.
Find dy/dx for the functions in Problems 1-5. 1. x2 = 2y2 - 4 = 0 2. x = y2 - 4y + 6 = 0 3. x2 = 4x + y2 - 3y + 1 = 0 4. x2 = 5x + y3 - 3y - 3 = 0 5. If x2 = y2 = 4, find y`.
In Exercises 13 through 20, use the chain rule to compute the derivative dy/dx for the given value of x. y ==;u= u 3 - 1 for x 2
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