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Partial derivatives answer?
z = (x^2 + 5x - 2y)^9
∂z / ∂x = ???
1 Answer
- llafferLv 74 months agoFavorite Answer
z = (x² + 5x - 2y)⁹
To get dz/dx, with other variables in place (y) we treat that as a constant.
We will need a chain rule so we can set that up below:
z = u⁹ and u = x² + 5x - 2y
Getting the derivative of each:
dz/du = 9u⁸ and du/dx = 2x + 5 (the constant term drops off)
so:
dz/dx = dz/du * du/dx
dz/dx = 9u⁸ (2x + 5)
Substituting the expression in terms of x and y instead of u:
dz/dx = 9(x² + 5x - 2y)⁸ (2x + 5)
