What is the derivative of-(10x/((x^2-4)^2)) ?

The derivative of-(10x/((x^2-4)^2)) is -(10(-3x^2-4))/((x^2-4)^3)

What is the first derivative of-(10x/((x^2-4)^2)) ?

The first derivative of-(10x/((x^2-4)^2)) is -(10(-3x^2-4))/((x^2-4)^3)

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\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 4 ) ^{2}})

- \frac{10 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 4 ) ^{2}})

Take the constant out:

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

= - 10 \frac{d}{d x} (\frac{x}{( x ^{2} - 4 ) ^{2}})

Apply the Quotient Rule:

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

= - 10 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 4 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 4 ) ^{2} ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

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

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

= - 10 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

Simplify

- 10 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}} : - \frac{10 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

= - \frac{10 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

f (x) = \frac{1}{x + 8}, at x = 9

n = 2 \sum \infty \frac{1}{n ^{3}}

\int \frac{x}{5 + 4 x - x ^{2}} d x

\int_{1}^{\infty} x^{2} d x

f (x) = \frac{2 x ^{2} + 6 x + 6}{x + 1}

What is the derivative of-(10x/((x^2-4)^2)) ?
The derivative of-(10x/((x^2-4)^2)) is -(10(-3x^2-4))/((x^2-4)^3)
What is the first derivative of-(10x/((x^2-4)^2)) ?
The first derivative of-(10x/((x^2-4)^2)) is -(10(-3x^2-4))/((x^2-4)^3)