What is (\partial)/(\partial x)(3e^{x/y}) ?

The answer to (\partial)/(\partial x)(3e^{x/y}) is (3e^{x/y})/y

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(\partial)/(\partial x)(3e^{x/y})

\frac{\partial}{\partial x} (3 e^{\frac{x}{y}})

\frac{3 e ^{\frac{x}{y}}}{y}

Solution steps

\frac{\partial}{\partial x} (3 e^{\frac{x}{y}})

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (e^{\frac{x}{y}})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

= 3 e^{\frac{x}{y}} \frac{1}{y}

Simplify

3 e^{\frac{x}{y}} \frac{1}{y} : \frac{3 e ^{\frac{x}{y}}}{y}

= \frac{3 e ^{\frac{x}{y}}}{y}

y = \frac{6}{x}, (1, \frac{6}{1})

\frac{d}{d x} (\frac{cos ( x )}{x})

(2 x y^{2} - 3) d x + (2 x^{2} y + 4) d y = 0

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

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 8)^{9})

What is (\partial)/(\partial x)(3e^{x/y}) ?
The answer to (\partial)/(\partial x)(3e^{x/y}) is (3e^{x/y})/y