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Answer :
Final answer:
The first partial derivatives of the function g(x, y) = x^7 * sin(y) are ∂g/∂x = 7x^6 * sin(y) and ∂g/∂y = x^7 * cos(y), making an option a) the correct choice.
Explanation:
The student has been asked to find the first partial derivatives of the function g(x, y) = x^7 * sin(y). To find the partial derivative of g concerning x, we hold y constant and differentiate g as if it were a function of x alone. Similarly, to find the partial derivative of g concerning y, we hold x constant and differentiate g as if it were a function of y alone.
For the partial derivative concerning x:
∂g/∂x = 7x^6 * sin(y),
and for the partial derivative concerning y:
∂g/∂y = x^7 * cos(y).
Therefore, the correct option from the given choices is a), which states:
- ∂g/∂x = 7x^6 * sin(y)
- ∂g/∂y = x^7 * cos(y)
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