What is (\partial)/(\partial x)(xcos(x+y)+y) ?

The answer to (\partial)/(\partial x)(xcos(x+y)+y) is -xsin(x+y)+cos(x+y)

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(\partial)/(\partial x)(xcos(x+y)+y)

\frac{\partial}{\partial x} (x cos (x + y) + y)

- x sin (x + y) + cos (x + y)

Solution steps

\frac{\partial}{\partial x} (x cos (x + y) + y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x cos (x + y)) = cos (x + y) - x sin (x + y)

\frac{\partial}{\partial x} (y) = 0

= cos (x + y) - x sin (x + y) + 0

Simplify

= - x sin (x + y) + cos (x + y)

\int_{- 2}^{0} (x - 2) (x + 1) d x

y = 8 x, y = \frac{5}{2} x, y = 9 - x^{2}

x \to 4 - lim (4 - x)

\frac{d y}{d x} = \frac{4}{x e ^{y}}

\int_{1}^{3} 11 r^{3} \cdot ln (r) d r

What is (\partial)/(\partial x)(xcos(x+y)+y) ?
The answer to (\partial)/(\partial x)(xcos(x+y)+y) is -xsin(x+y)+cos(x+y)