What is (\partial)/(\partial x)(x*y*cos(3x)+e^{xy}) ?

The answer to (\partial)/(\partial x)(x*y*cos(3x)+e^{xy}) is y(cos(3x)-3xsin(3x))+e^{xy}y

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(\partial)/(\partial x)(xycos(3x)+e^{xy})

\frac{\partial}{\partial x} (x \cdot y \cdot cos (3 x) + e^{x y})

y (cos (3 x) - 3 x sin (3 x)) + e^{x y} y

Solution steps

\frac{\partial}{\partial x} (x y cos (3 x) + e^{x y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y cos (3 x)) + \frac{\partial}{\partial x} (e^{x y})

\frac{\partial}{\partial x} (x y cos (3 x)) = y (cos (3 x) - 3 x sin (3 x))

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

= y (cos (3 x) - 3 x sin (3 x)) + e^{x y} y

x \to 0 lim (\frac{x - 12}{x - 4})

\int e^{3} x d x

\int 2 x e^{- x} d x

3 (x + 1), 4 (x + 1), x = 7

\int_{0}^{\infty} x e^{- x - y} d x

What is (\partial)/(\partial x)(x*y*cos(3x)+e^{xy}) ?
The answer to (\partial)/(\partial x)(x*y*cos(3x)+e^{xy}) is y(cos(3x)-3xsin(3x))+e^{xy}y