# Find the first partial derivatives of the function given a) in regards to x b) in regards to y f(x, y) = x^{7}y

Question
Derivatives
Find the first partial derivatives of the function given a) in regards to x b) in regards to y $$f(x, y) = x^{7}y$$

2020-11-09
To take a partial derivative you treat all variables as constants except for the one youre taking the derivative of. So
$$\frac{\partial}{\partial x}f(x,y)$$
$$=\frac{δ}{δx}(x^{7}y)$$
$$y\frac{δ}{δx}(x^{7})$$ [you factor out the y since its treated as constant in this case]
$$=7x^{6}y$$
$$b)\frac{δ}{δx}f(x,y)$$
$$=\frac{δ}{δx}(x^{7}y)$$
$$=x^{7}\frac{δ}{δx}(y)$$ [you factor out the x^{7} since its treated as constant in this case]
$$x=7$$

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