Question

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

Derivatives
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asked 2020-11-08
Find the first partial derivatives of the function given a) in regards to x b) in regards to y \(f(x, y) = x^{7}y\)

Answers (1)

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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