What is the derivative of-1/((5+x^2)) ?

The derivative of-1/((5+x^2)) is 2/((5+x)^3)

What is the first derivative of-1/((5+x^2)) ?

The first derivative of-1/((5+x^2)) is 2/((5+x)^3)

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

\frac{2}{( 5 + x ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( 5 + x ) ^{3}} \frac{d}{d x} (5 + x)

= - \frac{2}{( 5 + x ) ^{3}} \frac{d}{d x} (5 + x)

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

= - (- \frac{2}{( 5 + x ) ^{3}} \cdot 1)

Simplify

= \frac{2}{( 5 + x ) ^{3}}

x \to 0 lim (2 x^{2} - 10 x + 12)

\int sin (2 x + 3) d x

\int_{0}^{1} (x^{2} + 8) e^{- x} d x

y^{^{''}} + 49 y = 0, y (0) = 4, y^{^{''}} (0) = - 6

\int_{0}^{1} 4 (1 + x)^{4} d x

What is the derivative of-1/((5+x^2)) ?
The derivative of-1/((5+x^2)) is 2/((5+x)^3)
What is the first derivative of-1/((5+x^2)) ?
The first derivative of-1/((5+x^2)) is 2/((5+x)^3)