What is the derivative of ((1-x)/(2x)) ?

The derivative of ((1-x)/(2x)) is -1/(2x^2)

What is the first derivative of ((1-x)/(2x)) ?

The first derivative of ((1-x)/(2x)) is -1/(2x^2)

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\frac{d}{d x} (\frac{( 1 - x )}{2 x})

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

Solution steps

\frac{d}{d x} (\frac{( 1 - x )}{2 x})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{1 - x}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (1 - x) = - 1

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

= \frac{1}{2} \cdot \frac{( - 1 ) x - 1 \cdot ( 1 - x )}{x ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( - 1 ) x - 1 \cdot ( 1 - x )}{x ^{2}} : - \frac{1}{2 x ^{2}}

= - \frac{1}{2 x ^{2}}

y^{^{'}} = 0.19 y + 200

\int 5 e^{4} d x

y = x^{\frac{4}{7}} + 6 x

\frac{d}{d x} (x^{4} - 2 x^{3} + 3 x + 1)

What is the derivative of ((1-x)/(2x)) ?
The derivative of ((1-x)/(2x)) is -1/(2x^2)
What is the first derivative of ((1-x)/(2x)) ?
The first derivative of ((1-x)/(2x)) is -1/(2x^2)