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

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

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

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

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\frac{d}{d x} (\frac{C ^{2} - x ^{2}}{2 x})

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

Solution steps

\frac{d}{d x} (\frac{C ^{2} - x ^{2}}{2 x})

Treat

C

as a constant

Take the constant out:

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

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

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

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

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

Simplify

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

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

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