What is the derivative of 2/(x^2+5) ?

The derivative of 2/(x^2+5) is -(4x)/((x^2+5)^2)

What is the first derivative of 2/(x^2+5) ?

The first derivative of 2/(x^2+5) is -(4x)/((x^2+5)^2)

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\frac{d}{d x} (\frac{2}{x ^{2} + 5})

- \frac{4 x}{( x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2}{x ^{2} + 5})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{x ^{2} + 5})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 2 \frac{d}{d x} ((x^{2} + 5)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 5 ) ^{2}} \frac{d}{d x} (x^{2} + 5)

= - \frac{1}{( x ^{2} + 5 ) ^{2}} \frac{d}{d x} (x^{2} + 5)

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

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

Simplify

2 (- \frac{1}{( x ^{2} + 5 ) ^{2}} \cdot 2 x) : - \frac{4 x}{( x ^{2} + 5 ) ^{2}}

= - \frac{4 x}{( x ^{2} + 5 ) ^{2}}

x \to 5 lim (\frac{x + 1}{x - 5})

(x^{2} - 8)^{4}, at x = 3

f (x) = 7 + 4 x^{2} - 2 x^{3}, at x = 1

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

\frac{d}{d x} (\frac{x}{x - 1})

What is the derivative of 2/(x^2+5) ?
The derivative of 2/(x^2+5) is -(4x)/((x^2+5)^2)
What is the first derivative of 2/(x^2+5) ?
The first derivative of 2/(x^2+5) is -(4x)/((x^2+5)^2)