What is the d/(dy)((x)(xe^{y/x}+ye^{x/y})) ?

The d/(dy)((x)(xe^{y/x}+ye^{x/y})) is x(e^{y/x}+e^{x/y}-(xe^{x/y})/y)

What is the first d/(dy)((x)(xe^{y/x}+ye^{x/y})) ?

The first d/(dy)((x)(xe^{y/x}+ye^{x/y})) is x(e^{y/x}+e^{x/y}-(xe^{x/y})/y)

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Popular >

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d y} (x e^{\frac{y}{x}}) = e^{\frac{y}{x}}

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

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

a^{2} + 6 a + 9 - (a + 4) (a + 2)^{'}

(5 x + 3) d e

\frac{d}{d t} ((s) (\frac{3}{4 π} cos (4 t) + \frac{3}{7 π} sin (7 t)))

\frac{1}{2 ( x + 7 )}

- 5 (\frac{- 5 - 3 y}{10} - 4 y = 10)

What is the d/(dy)((x)(xe^{y/x}+ye^{x/y})) ?
The d/(dy)((x)(xe^{y/x}+ye^{x/y})) is x(e^{y/x}+e^{x/y}-(xe^{x/y})/y)
What is the first d/(dy)((x)(xe^{y/x}+ye^{x/y})) ?
The first d/(dy)((x)(xe^{y/x}+ye^{x/y})) is x(e^{y/x}+e^{x/y}-(xe^{x/y})/y)