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

The answer to (\partial)/(\partial x)(xsin(x+y)-cos(x+y)) is xcos(x+y)+2sin(x+y)

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

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

x cos (x + y) + 2 sin (x + y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= x cos (x + y) + 2 sin (x + y)

y^{^{'}} = y^{4} \cdot (4 x^{2} + x)

(7, 4), (1, - 2)

\int (x^{2} - 2 x)^{2} d x

\int \frac{3}{( 4 + x ^{2} )} d x

5 t sin (4 t)

What is (\partial)/(\partial x)(xsin(x+y)-cos(x+y)) ?
The answer to (\partial)/(\partial x)(xsin(x+y)-cos(x+y)) is xcos(x+y)+2sin(x+y)