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

The derivative of ce^{y/x} is (ce^{y/x}(x\frac{dy)/(dx)-y)}{x^2}

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

The first derivative of ce^{y/x} is (ce^{y/x}(x\frac{dy)/(dx)-y)}{x^2}

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{\partial}{\partial x} (x + y + ∣ x ∣^{3} y^{2})

\frac{d}{d x} (5 x^{2 π})

(\frac{10 - ( 2 )}{( x )}) \cdot (\frac{3 + ( 1 )}{( x )})

(\frac{1}{1 + e ^{x}})^{^{'}}

- 3 x x + 1

What is the derivative of ce^{y/x} ?
The derivative of ce^{y/x} is (ce^{y/x}(x\frac{dy)/(dx)-y)}{x^2}
What is the first derivative of ce^{y/x} ?
The first derivative of ce^{y/x} is (ce^{y/x}(x\frac{dy)/(dx)-y)}{x^2}