What is (\partial)/(\partial x)(-xe^xsin(y)) ?

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

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(\partial)/(\partial x)(-xe^xsin(y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

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

= - sin (y) (1 \cdot e^{x} + e^{x} x)

Simplify

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

f (x) = x^{2} + 91 x - 92, at x = 2

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

f (x) = (\frac{x + 7}{x - 7})^{5}

x^{2} - 1, - x + 2, x = 0, x = 1

\int \frac{6 + x + x}{x} d x

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