What is the derivative of (x^2/(x^2-25)) ?

The derivative of (x^2/(x^2-25)) is -(50x)/((x^2-25)^2)

What is the first derivative of (x^2/(x^2-25)) ?

The first derivative of (x^2/(x^2-25)) is -(50x)/((x^2-25)^2)

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\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 25})

- \frac{50 x}{( x ^{2} - 25 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 25})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} - 25 ) - \frac{d}{d x} ( x ^{2} - 25 ) x ^{2}}{( x ^{2} - 25 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 25) = 2 x

= \frac{2 x ( x ^{2} - 25 ) - 2 x x ^{2}}{( x ^{2} - 25 ) ^{2}}

Simplify

\frac{2 x ( x ^{2} - 25 ) - 2 x x ^{2}}{( x ^{2} - 25 ) ^{2}} : - \frac{50 x}{( x ^{2} - 25 ) ^{2}}

= - \frac{50 x}{( x ^{2} - 25 ) ^{2}}

\int \frac{( 1 + y ^{2} )}{y} d y

x^{2} + a x + b

\frac{d}{d x} (4 cos (π x))

\frac{693 x ^{\frac{5}{2}}}{8}

(x, y) \to (0, 0) lim (x y)

What is the derivative of (x^2/(x^2-25)) ?
The derivative of (x^2/(x^2-25)) is -(50x)/((x^2-25)^2)
What is the first derivative of (x^2/(x^2-25)) ?
The first derivative of (x^2/(x^2-25)) is -(50x)/((x^2-25)^2)