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

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

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

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

- sin (y) + e^{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

y^{^{''}} - 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 7

x \to \infty lim (\frac{1}{8})

f (x) = \frac{3}{4 x + 1}, (- 1, - 1)

f (x) = \frac{( x ^{2} + 1 )}{( x ^{2} - 1 )}

x + y^{2} = 20, x + y = 0

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