What is (\partial)/(\partial x)(xy-xsin(y)) ?

The answer to (\partial)/(\partial x)(xy-xsin(y)) is y-sin(y)

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(\partial)/(\partial x)(xy-xsin(y))

\frac{\partial}{\partial x} (x y - x sin (y))

y - sin (y)

Solution steps

\frac{\partial}{\partial x} (x y - x sin (y))

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 sin (y))

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

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

= y - sin (y)

\frac{( t ^{2} + 1 ) ^{\frac{3}{2}}}{3}^{^{'}}

\frac{d}{d x} ((x + 2) (x - 2)^{3})

- 7 (6 x^{2} + 7)^{- 6}

\frac{c ^{4} - x ^{4}}{c ^{4} + x ^{4}}

\int sin (x^{3}) x^{2} d x

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