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

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

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(\partial)/(\partial x)(xz-e^xsin(y))

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

z - sin (y) e^{x}

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

x \to - 2 lim (\frac{5 x ^{2} + 6}{x})

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

y = \frac{1}{4 x ^{2}}, y = x, y = \frac{x}{10}

\frac{d}{d x} (\frac{x - 1}{x ^{2} + 4})

x^{2} \frac{d y}{d x} = x y + 3 y^{2}

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