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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (y - x)

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

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

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

= 1 \cdot cos (y - x) + sin (y - x) x

Simplify

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

x \to 1 lim ((x - 1))

\int_{- 3}^{0} \frac{1}{9 - x ^{2}} d x

\frac{\partial}{\partial y} (e^{x y} sin (y))

\int_{0}^{20} cos (π x) d x

\int ln (x - 5) d x

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