What is (\partial)/(\partial x)((c^2-x^2)/(2x)) ?

The answer to (\partial)/(\partial x)((c^2-x^2)/(2x)) is (-x^2-c^2)/(2x^2)

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(\partial)/(\partial x)((c^2-x^2)/(2x))

\frac{\partial}{\partial x} (\frac{c ^{2} - x ^{2}}{2 x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{c ^{2} - x ^{2}}{2 x})

Take the constant out:

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

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

\frac{\partial}{\partial x} (c^{2} - x^{2}) = - 2 x

\frac{\partial}{\partial x} (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}}

\int \frac{1}{( x ^{2} + 25 ) ^{\frac{5}{2}}} d x

f (t) = e^{t a n (π t)}

y = \frac{6 x ^{2} + 2 x + 6}{x}

\frac{d y}{d x} - 2 x y = 10 x

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

What is (\partial)/(\partial x)((c^2-x^2)/(2x)) ?
The answer to (\partial)/(\partial x)((c^2-x^2)/(2x)) is (-x^2-c^2)/(2x^2)