Suppose you have inputs as x, y, and z with values -2, 5, and -4 respectively. You have a neuron ‘q’ and neuron ‘f’ with functions:q = x + y f = q * zThe graphical representation of the functions is as follows: What is the gradient of F with respect to x, y, and z?(HINT: To calculate the gradient, you must find (df/dx), (df/dy) and (df/dz)).Question 18Select one:A.(-3,4,4)B.(3,-4,-4)C.(-4,-4,3)D.(4,4,3)
Question
Suppose you have inputs as x, y, and z with values -2, 5, and -4 respectively. You have a neuron ‘q’ and neuron ‘f’ with functions:q = x + y f = q * zThe graphical representation of the functions is as follows: What is the gradient of F with respect to x, y, and z?(HINT: To calculate the gradient, you must find (df/dx), (df/dy) and (df/dz)).Question 18Select one:A.(-3,4,4)B.(3,-4,-4)C.(-4,-4,3)D.(4,4,3)
Solution
To find the gradient of F with respect to x, y, and z, we need to calculate the partial derivatives df/dx, df/dy, and df/dz.
First, let's find df/dx. Since f = q * z and q = x + y, we can substitute q into the equation for f to get f = (x + y) * z. The derivative of f with respect to x is then df/dx = z.
Second, let's find df/dy. Again, since f = (x + y) * z, the derivative of f with respect to y is also df/dy = z.
Finally, let's find df/dz. Since f = q * z, the derivative of f with respect to z is df/dz = q.
Substituting the given values for x, y, and z into these equations gives us df/dx = -4, df/dy = -4, and df/dz = 3.
So, the gradient of F with respect to x, y, and z is (-4, -4, 3), which is not an option in the given choices. There might be a mistake in the question or the options provided.
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