What is (\partial)/(\partial x)(xe^y+cos(xy)) ?

The answer to (\partial)/(\partial x)(xe^y+cos(xy)) is e^y-sin(xy)y

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(\partial)/(\partial x)(xe^y+cos(xy))

\frac{\partial}{\partial x} (x e^{y} + cos (x y))

e^{y} - sin (x y) y

Solution steps

\frac{\partial}{\partial x} (x e^{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 e^{y}) + \frac{\partial}{\partial x} (cos (x y))

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

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

= e^{y} - sin (x y) y

\int \frac{5}{y} d y

\frac{d}{d x} (5 cos (3 x))

n = 1 \sum \infty (cos (28))^{n}

\frac{( s + 3 )}{( ( s + 3 ) ^{2} + 25 )}

What is (\partial)/(\partial x)(xe^y+cos(xy)) ?
The answer to (\partial)/(\partial x)(xe^y+cos(xy)) is e^y-sin(xy)y