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

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

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

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

- \frac{x}{y ^{2}} + e^{y}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (\frac{x}{y}) = - \frac{x}{y ^{2}}

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

= - \frac{x}{y ^{2}} + e^{y}

f (x) = - 3 cos (x), at x = \frac{3 π}{4}

\frac{d}{d x} (sin (w x))

\int 15 sec^{4} (x) d x

f (x) = x^{2} - 9, (- 5, 16)

tan (x) - 1

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