What is the derivative of f(x)=(20x)/(x^2-5) ?

The derivative of f(x)=(20x)/(x^2-5) is (20(-x^2-5))/((x^2-5)^2)

What is the first derivative of f(x)=(20x)/(x^2-5) ?

The first derivative of f(x)=(20x)/(x^2-5) is (20(-x^2-5))/((x^2-5)^2)

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derivative of

f (x) = \frac{20 x}{x ^{2} - 5}

\frac{20 ( - x ^{2} - 5 )}{( x ^{2} - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{20 x}{x ^{2} - 5})

Take the constant out:

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

= 20 \frac{d}{d x} (\frac{x}{x ^{2} - 5})

Apply the Quotient Rule:

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

= 20 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 5 ) - \frac{d}{d x} ( x ^{2} - 5 ) x}{( x ^{2} - 5 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 5) = 2 x

= 20 \cdot \frac{1 \cdot ( x ^{2} - 5 ) - 2 xx}{( x ^{2} - 5 ) ^{2}}

Simplify

20 \cdot \frac{1 \cdot ( x ^{2} - 5 ) - 2 xx}{( x ^{2} - 5 ) ^{2}} : \frac{20 ( - x ^{2} - 5 )}{( x ^{2} - 5 ) ^{2}}

= \frac{20 ( - x ^{2} - 5 )}{( x ^{2} - 5 ) ^{2}}

What is the derivative of f(x)=(20x)/(x^2-5) ?
The derivative of f(x)=(20x)/(x^2-5) is (20(-x^2-5))/((x^2-5)^2)
What is the first derivative of f(x)=(20x)/(x^2-5) ?
The first derivative of f(x)=(20x)/(x^2-5) is (20(-x^2-5))/((x^2-5)^2)