Question

Find the partial derivative ∂z/∂x of the function z=(x² x-y)⁷.

Answer 1

To find the partial derivative ∂z/∂x of the function z=(x² x-y)⁷, differentiate each term with respect to x while treating y as a constant. Finally, raise the differentiated terms to the power of 7 and multiply them together.

Step-by-step explanation:

To find the partial derivative ∂z/∂x of the function z=(x² x-y)⁷, we need to differentiate each term with respect to x while treating y as a constant.

First, we differentiate x² with respect to x, which is 2x.

Next, we differentiate x with respect to x, which is 1.

The derivative of y with respect to x is 0 since y is treated as a constant.

Finally, we raise the differentiated terms to the power of 7 and multiply them together to get (∂z/∂x) = 7x^(2) * 1 * (x-y)^(6).