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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

x^{^{''}} + 9 x - 27 = 0, x (0) = 4, x^{^{'}} (0) = 6

\int \frac{1}{12 y} d y

\frac{\partial}{\partial y} (\frac{y - t}{5 y + 2 t})

t - π

\int \frac{x ^{2}}{( x ^{2} + 1 ) ^{2}} d x

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