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

Question

Find the gradients of the following functions:(a) f (x, y, z) = x2 + y3 + z4 .(b) f (x, y, z) = x2 y3 z4 .(c) f (x, y, z) = e x sin(y) ln(z)
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Solution 1

Sure, let's find the gradients of the given functions.

(a) f (x, y, z) = x^2 + y^3 + z^4

The gradient of a function is a vector of its partial derivatives. So, we need to find the partial derivatives of f with respect to x, y, and z.

∂f/∂x = 2x ∂f/∂y = 3y^2 ∂f/∂z = 4z^3

So, the gradient of f is Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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