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

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

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

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

x cos (y - x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (y - x) = 1

= x cos (y - x) \cdot 1

Simplify

= x cos (y - x)

\frac{d}{d x} (x y + y - 1)

\int_{4}^{5} \frac{1}{( x - 4 ) ^{\frac{4}{3}}} d x

f (x) = e^{x + 2} + 1

\frac{d}{d x} (\frac{x ^{2} - 2}{x - 1})

x \to 0 lim (ln ∣ x ∣)

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