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

The answer to (\partial)/(\partial x)(xsin(x)+ysin(y)) is xcos(x)+sin(x)

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(\partial)/(\partial x)(xsin(x)+ysin(y))

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

x cos (x) + sin (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y sin (y)) = 0

= sin (x) + x cos (x) + 0

Simplify

= x cos (x) + sin (x)

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\int_{- 2}^{3} \frac{50}{x ^{4}} d x

\int x sin (k w x) d x

\int_{0}^{2 π} sin (x) sin (x + 1) d x

\int 2 v d v

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