What is (\partial)/(\partial x)(yx+2x+{g}(y)) ?

The answer to (\partial)/(\partial x)(yx+2x+{g}(y)) is y+2+(\partial)/(\partial x)({g}(y))

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(\partial)/(\partial x)(yx+2x+{g}(y))

\frac{\partial}{\partial x} (y x + 2 x + g (y))

y + 2 + \frac{\partial}{\partial x} (g (y))

Solution steps

\frac{\partial}{\partial x} (y x + 2 x + g (y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 x) = 2

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

y^{^{'}} = - x y

f (x) = x^{3} - 2 x + 2, at x = 3

\frac{\partial}{\partial x} (ln (a x + b y) + c^{x + y})

\int \frac{cos ( x )}{sin ^{2} ( x )} d x

\int e^{2 x} - e^{x} d x

What is (\partial)/(\partial x)(yx+2x+{g}(y)) ?
The answer to (\partial)/(\partial x)(yx+2x+{g}(y)) is y+2+(\partial)/(\partial x)({g}(y))