# Find the first partial derivatives of the function. f(x, y) = x^{9}y

**Solution:**

∂f(xy)/∂x and ∂f(xy)/∂y are the first partial derivatives of the given function.

∂f(xy)/∂x = ∂x^{9}y/∂x

= y∂x^{9}/∂x + x^{9}∂y/∂x

While differentiating partially with respect to x, y becomes a constant and therefore,

∂f(xy)/∂x = y(9)x^{8} + ( x^{9})(0)

= 9yx^{8 }+ 0

= 9yx⁸

∂f(xy)/∂y = ∂x^{9}y/∂y

= x^{9}∂y/∂y + y∂x^{9}/∂y

Since partial differentiation is w.r.t. y then x becomes a constant

∂f(xy)/∂y = x^{9} + y(0) = x^{9}

## Find the first partial derivatives of the function. f(x, y) = x^{9}y

**Summary:**

The first partial derivatives of the function. f(x, y) = x^{9}y are ∂f(xy)/∂x = 9yx^{8} and ∂f(xy)/∂y = x^{9}

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