What is (\partial)/(\partial x)(5x+y(x^2+y^2)) ?

The answer to (\partial)/(\partial x)(5x+y(x^2+y^2)) is 5+2yx

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(\partial)/(\partial x)(5x+y(x^2+y^2))

\frac{\partial}{\partial x} (5 x + y (x^{2} + y^{2}))

5 + 2 y x

Solution steps

\frac{\partial}{\partial x} (5 x + y (x^{2} + y^{2}))

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (y (x^{2} + y^{2}))

\frac{\partial}{\partial x} (5 x) = 5

\frac{\partial}{\partial x} (y (x^{2} + y^{2})) = 2 y x

= 5 + 2 y x

\int e^{x} - 2 cos (x) d x

y = ln (7 - 9 x^{2} + 8 x^{4}), at x = 1

y = x^{2} + 3, (- 3, 12)

n = 1 \sum \infty \frac{1}{( - 3 ) ^{n}}

\frac{d}{d x} (\frac{2 x ^{2} + 4 x + 8}{x})

What is (\partial)/(\partial x)(5x+y(x^2+y^2)) ?
The answer to (\partial)/(\partial x)(5x+y(x^2+y^2)) is 5+2yx