What is the derivative of-(250x/((25x^2+1)^2)) ?

The derivative of-(250x/((25x^2+1)^2)) is -(250(1-75x^2))/((25x^2+1)^3)

What is the first derivative of-(250x/((25x^2+1)^2)) ?

The first derivative of-(250x/((25x^2+1)^2)) is -(250(1-75x^2))/((25x^2+1)^3)

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\frac{d}{d x} (- \frac{250 x}{( 25 x ^{2} + 1 ) ^{2}})

- \frac{250 ( 1 - 75 x ^{2} )}{( 25 x ^{2} + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{250 x}{( 25 x ^{2} + 1 ) ^{2}})

Take the constant out:

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

= - 250 \frac{d}{d x} (\frac{x}{( 25 x ^{2} + 1 ) ^{2}})

Apply the Quotient Rule:

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

= - 250 \cdot \frac{\frac{d x}{d x} ( 25 x ^{2} + 1 ) ^{2} - \frac{d}{d x} ( ( 25 x ^{2} + 1 ) ^{2} ) x}{( ( 25 x ^{2} + 1 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((25 x^{2} + 1)^{2}) = 100 x (25 x^{2} + 1)

= - 250 \cdot \frac{1 \cdot ( 25 x ^{2} + 1 ) ^{2} - 100 x ( 25 x ^{2} + 1 ) x}{( ( 25 x ^{2} + 1 ) ^{2} ) ^{2}}

Simplify

- 250 \cdot \frac{1 \cdot ( 25 x ^{2} + 1 ) ^{2} - 100 x ( 25 x ^{2} + 1 ) x}{( ( 25 x ^{2} + 1 ) ^{2} ) ^{2}} : - \frac{250 ( 1 - 75 x ^{2} )}{( 25 x ^{2} + 1 ) ^{3}}

= - \frac{250 ( 1 - 75 x ^{2} )}{( 25 x ^{2} + 1 ) ^{3}}

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

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

\int_{1}^{4} \frac{x}{x - 9} d x

\frac{d}{d x} (\frac{1}{82} e^{x})

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

What is the derivative of-(250x/((25x^2+1)^2)) ?
The derivative of-(250x/((25x^2+1)^2)) is -(250(1-75x^2))/((25x^2+1)^3)
What is the first derivative of-(250x/((25x^2+1)^2)) ?
The first derivative of-(250x/((25x^2+1)^2)) is -(250(1-75x^2))/((25x^2+1)^3)