What is (\partial)/(\partial y)(cos(y)e^x+2/x) ?

The answer to (\partial)/(\partial y)(cos(y)e^x+2/x) is -e^xsin(y)

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(\partial)/(\partial y)(cos(y)e^x+2/x)

\frac{\partial}{\partial y} (cos (y) e^{x} + \frac{2}{x})

- e^{x} sin (y)

Solution steps

\frac{\partial}{\partial y} (cos (y) e^{x} + \frac{2}{x})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (cos (y) e^{x}) + \frac{\partial}{\partial y} (\frac{2}{x})

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

\frac{\partial}{\partial y} (\frac{2}{x}) = 0

= - e^{x} sin (y) + 0

Simplify

= - e^{x} sin (y)

x^{2} (x^{3} - 1)

x \to 0 lim (\frac{b - c}{x ^{a}})

4 + 6 x

9

What is (\partial)/(\partial y)(cos(y)e^x+2/x) ?
The answer to (\partial)/(\partial y)(cos(y)e^x+2/x) is -e^xsin(y)