What is (\partial)/(\partial x)((e^x-x)sin(y)) ?

The answer to (\partial)/(\partial x)((e^x-x)sin(y)) is sin(y)(e^x-1)

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(\partial)/(\partial x)((e^x-x)sin(y))

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

sin (y) (e^{x} - 1)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

x y^{2} \frac{d y}{d x} = y^{3} - x^{3}, y (1) = 2

x \to 1 lim (x (x + 1))

\frac{d}{d x} (\frac{x}{2} x^{2} - 1)

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

\frac{d}{d x} (\frac{6 x}{3 - cot ( x )})

What is (\partial)/(\partial x)((e^x-x)sin(y)) ?
The answer to (\partial)/(\partial x)((e^x-x)sin(y)) is sin(y)(e^x-1)