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

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

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

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

e^{x} - sin (y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x} - sin (y)

\frac{6 x ^{2} + 4 x + 2}{x}

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

x \to + 1 lim (\frac{1 - x}{x ^{2} - 1})

\int_{0}^{1} x e^{- 6 x^{2}} d x

\frac{\partial}{\partial x} (e^{- 7 t} cos (π x))

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