What is the derivative of-xe^{y/x} ?

The derivative of-xe^{y/x} is -e^{y/x}-(e^{y/x}(x(dy)/(dx)-y))/x

What is the first derivative of-xe^{y/x} ?

The first derivative of-xe^{y/x} is -e^{y/x}-(e^{y/x}(x(dy)/(dx)-y))/x

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Popular >

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{\frac{y}{x}}

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

\frac{d x}{d x} = 1

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

= - 1 \cdot e^{\frac{y}{x}} + \frac{e ^{\frac{y}{x}} ( x \frac{d y}{d x} - y )}{x ^{2}} x

Simplify

- 1 \cdot e^{\frac{y}{x}} + \frac{e ^{\frac{y}{x}} ( x \frac{d y}{d x} - y )}{x ^{2}} x : - e^{\frac{y}{x}} - \frac{e ^{\frac{y}{x}} ( x \frac{d y}{d x} - y )}{x}

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

\int_{0}^{\frac{π}{2}} cot (x) d x

x \to 0 lim ((1 + 8 x)^{\frac{6}{x}})

\frac{4 - 3 x - x ^{2}}{x ^{2} - 1}

\frac{d x}{d y} = 3 x

\int_{\frac{1}{2}}^{3} \frac{1}{x ^{2}} d x

What is the derivative of-xe^{y/x} ?
The derivative of-xe^{y/x} is -e^{y/x}-(e^{y/x}(x(dy)/(dx)-y))/x
What is the first derivative of-xe^{y/x} ?
The first derivative of-xe^{y/x} is -e^{y/x}-(e^{y/x}(x(dy)/(dx)-y))/x