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

The derivative of (c^2-x^2/(c^2+x^2)) is -(4c^2x)/((c^2+x^2)^2)

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

The first derivative of (c^2-x^2/(c^2+x^2)) is -(4c^2x)/((c^2+x^2)^2)

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

- \frac{4 c ^{2} x}{( c ^{2} + x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (c^{2} + x^{2}) = 2 x

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

Simplify

\frac{( - 2 x ) ( c ^{2} + x ^{2} ) - 2 x ( c ^{2} - x ^{2} )}{( c ^{2} + x ^{2} ) ^{2}} : - \frac{4 c ^{2} x}{( c ^{2} + x ^{2} ) ^{2}}

= - \frac{4 c ^{2} x}{( c ^{2} + x ^{2} ) ^{2}}

y = x sin (\frac{5}{x})

f (x) = \frac{cos ( x )}{2 + sin ( x )}

\int cos^{3} (8 - x) sin (8 - x) d x

\frac{d y}{d x}, x y = 5

n = 0 \sum \infty (\frac{5}{6})^{n}

What is the derivative of (c^2-x^2/(c^2+x^2)) ?
The derivative of (c^2-x^2/(c^2+x^2)) is -(4c^2x)/((c^2+x^2)^2)
What is the first derivative of (c^2-x^2/(c^2+x^2)) ?
The first derivative of (c^2-x^2/(c^2+x^2)) is -(4c^2x)/((c^2+x^2)^2)